/ calcule matrice Fie matricele A=#A şi B=#B. Precizaţi care este matricea A²+ 2·A·B + B²(unde A²=A·A).

]]> 1.0000000 1.0000000 0 true true abc #solutie1

]]> Răspuns corect!

]]> #solutie2

]]> Răspuns greşit!

]]> #solutie3

]]> Răspuns greşit!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie1</mi><mo>=</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>+</mo><msup><mi>B</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie2</mi><mo>=</mo><mn>2</mn><mo>*</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>B</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie3</mi><mo>=</mo><mn>3</mn><mo>*</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>+</mo><mn>3</mn><mo>*</mo><msup><mi>B</mi><mn>2</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> calcule transpusa Fie matricea A=#A. Precizaţi care este matricea «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«msup»«mi mathvariant=¨normal¨»A«/mi»«mi mathvariant=¨normal¨»T«/mi»«/msup»«/mfenced»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi mathvariant=¨normal¨»A«/mi»«/math».

]]> 1.0000000 1.0000000 0 true true abc #solutie1

]]> Răspuns corect!

]]> #solutie2

]]> Răspuns greşit!

]]> #solutie3

]]> Răspuns greşit!

]]> 1.0000000 1.0000000 0 true true abc #solutie1

]]> Răspuns corect!

]]> #solutie2

]]> Răspuns greşit!

]]> #solutie3

]]> Răspuns greşit

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>b</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>c</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>d</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie1</mi><mo>=</mo><mi>m</mi><mo>*</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>*</mo><mi>A</mi><mo>+</mo><mi>p</mi><mo>*</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><msup><mi>A</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>*</mo><mi>A</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>p</mi><mo>*</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie3</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>*</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><mi>n</mi><mo>*</mo><mi>A</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>p</mi><mo>*</mo><mi>I</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> mai multe operatii cu matrice Date matricele A=#A şi B=#B alegeţi raspunsul corect pentru operaţiile de mai jos:

]]> 1.0000000 1.0000000 0 true Raspuns corect!

]]> Mai calculează!

]]> Răspuns greşit!

]]> Suma A+B este:

]]> #suma Produsul A·B este:

]]> #produs Matricea A² este:

]]> #patrat1 Matricea B² este:

]]> #patrat2 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>A</mi><mo>+</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>produs</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>patrat1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>patrat2</mi><mo>=</mo><mi>B</mi><mo>*</mo><mi>B</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> matrice recapitulare 2 Fie matricele A=#A şi B=#B. Se consideră funcţia liniară «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»f«/mi»«mo»:«/mo»«msub»«mi mathvariant=¨normal¨»M«/mi»«mn»2«/mn»«/msub»«mfenced»«mi mathvariant=¨normal¨»§#8477;«/mi»«/mfenced»«mo»§#8594;«/mo»«msub»«mi mathvariant=¨normal¨»M«/mi»«mn»2«/mn»«/msub»«mfenced»«mi mathvariant=¨normal¨»§#8477;«/mi»«/mfenced»«mo»§#160;«/mo»«/math», f(X)=a·X+b·I₂, unde a=#m şi b=#n. Pentru aplicaţiile de mai jos, asociaţi matricea răspuns corectă.

]]> 1.0000000 1.0000000 0 true Răspuns corect!

]]> Mai calculează!

]]> Răspuns greşit!

]]> f(A)+f(B)

]]> #solutie1 f(A · B)

]]> #solutie2 f(A) · f(B)

]]> #solutie3 f(A+B)

]]> #solutie4 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>c</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>d</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>A</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi><mo>+</mo><mi>m</mi><mo>*</mo><mi>B</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie3</mi><mo>=</mo><mo>(</mo><mi>m</mi><mo>*</mo><mi>A</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>m</mi><mo>*</mo><mi>B</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie4</mi><mo>=</mo><mi>m</mi><mo>*</mo><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo><mo>+</mo><mi>n</mi><mo>*</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Operaţii cu matrice Fie matricele:

Atunci
A + B este:

]]> 1.0000000 0.3333333 0 0 0 0 «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> Operaţii cu matrice Fie matricele:

«math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mi»§#351;i«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Atunci A+B este:

]]> 1.0000000 0.3333333 0 0 0 0 «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> Operaţii cu matrice Înmulţirea matricelor este operaţie comutativă.

]]> 1.0000000 1.0000000 0 true Mai gândeşte-te!

]]> false Corect!

]]> Operaţii cu matrice Fie matricele:

«math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mi»§#351;i«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math».

Să se calculeze matricea 2A²+B².

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mn»11«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»8«/mn»«/mtd»«mtd»«mn»19«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»20«/mn»«/mtd»«mtd»«mn»8«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> 2.0000000 1.0000000 0 0 11-2-3-81972-208]]> Răspuns corect.

]]> <question><correctAnswers><correctAnswer>M</correctAnswer><correctAnswer id="1">N</correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>11</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>8</mn></mtd><mtd><mn>19</mn></mtd><mtd><mn>7</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mo>-</mo><mn>20</mn></mtd><mtd><mn>8</mn></mtd></mtr></mtable></mfenced></math>]]></correctAnswer><correctAnswer id="3"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="2"/><assertion name="equivalent_symbolic" correctAnswer="2"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Operaţii cu matrice Adunarea matricelor este operaţie comutativă.

]]> 1.0000000 1.0000000 0 true Corect!

]]> false Mai gândeşte-te!

]]> operaţii cu matrice Fie matricele:

«math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mi»§#351;i«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math».

Să se calculeze A·B.

]]> Răspunsul corect este: «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»9«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»5«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 1.0000000 0 0 44-59-48-2-56 ]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>4</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mn>9</mn></mtd><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn></mtd><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mn>6</mn></mtd></mtr></mtable></mfenced><mo> </mo></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Operaţii cu matrice Fie matricele:

«math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mi»§#351;i«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Atunci matricea 2A+3B este:

]]> Un singur răspuns corect

]]> 1.0000000 1.0000000 0 true true abc «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> Răspuns incorect!

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»7«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> Răspuns incorect!

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»7«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> Răspuns incorect!

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»7«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> Răspuns corect!

]]> <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> Operaţii cu matrice Fie matricele:

Atunci A+B este:

]]> (un singur răspuns este corect)

]]> 1.0000000 1.0000000 0 true true abc «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> Răspuns incorect!

]]> Răspuns corect!

]]> «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»A«/mi»«mo»+«/mo»«mi mathvariant=¨normal¨»B«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> Răspuns incorect!

]]> <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> Operaţii cu matrice Fie matricele:

Se notează:

«math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»M«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»; «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»N«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mn»9«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»7«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»15«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»; «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»P«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»7«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»15«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»12«/mn»«/mtd»«mtd»«mn»31«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»; «math style=¨font-size:14px¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»Q«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»9«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math».

Asociaţi operaţiilor de mai jos matricea corespunzătoare dintre M, N, P şi Q.

]]> 2.0000000 1.0000000 0 true Răspuns corect!

]]> Mai calculează!

]]> Răspuns incorect!

]]> A·B este:

]]> N A+B este:

]]> M B²este:

]]> Q A²este:

]]> P <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> A²=A·A

]]> recapitulare matrice Asociaţi matricelor A=#A şi B=#B matricea răspuns corectă pentru operaţiile de mai jos:

]]> 1.0000000 1.0000000 0 true 2 · A · B - 3 · B · A

]]> #solutie4

]]> 3A - 2B

]]> #solutie1 A · A^T+ B · B^T

]]> #solutie2 A² + B²

]]> #solutie3 2 · A · B - 3 · B · A

]]> #solutie4 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie1</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>A</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie2</mi><mo>=</mo><mi>A</mi><mo>*</mo><msup><mi>A</mi><mo>T</mo></msup><mo>+</mo><mi>B</mi><mo>*</mo><msup><mi>B</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie3</mi><mo>=</mo><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><msup><mi>B</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie4</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>A</mi><mo>*</mo><mi>B</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>B</mi><mo>*</mo><mi>A</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Recapitulare transpusa Fie matricele A=#A, B=#B şi C=#C. Pentru operaţiile de mai jos alegeţi matricea răpsuns corespunzătoare.

]]> 1.0000000 1.0000000 0 true (A+B)^T+ C^T

]]> #solutie1 (A · B)^T + (C · A)^T

]]> #solutie2 (A^T + B)^T + (C^T)^T

]]> #solutie3 (A^T)^T+ B + C^T

]]> #solutie4 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>b</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie1</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><msup><mo>)</mo><mo>T</mo></msup><mo>+</mo><msup><mi>C</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie2</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>*</mo><mi>B</mi><msup><mo>)</mo><mo>T</mo></msup><mo>+</mo><mo>(</mo><mi>C</mi><mo>*</mo><mi>A</mi><msup><mo>)</mo><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie3</mi><mo>=</mo><mo>(</mo><msup><mi>A</mi><mo>T</mo></msup><mo>+</mo><mi>B</mi><msup><mo>)</mo><mo>T</mo></msup><mo>+</mo><mo>(</mo><msup><mi>C</mi><mo>T</mo></msup><msup><mo>)</mo><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solutie4</mi><mo>=</mo><mo>(</mo><msup><mi>A</mi><mo>T</mo></msup><msup><mo>)</mo><mo>T</mo></msup><mo>+</mo><mi>B</mi><mo>+</mo><msup><mi>C</mi><mo>T</mo></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> suma matricelor1 Date matricele A=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»M«/mi»«/math» şi B=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»N«/mi»«/math» precizaţi care este matricea A · B.

]]> Suma matricelor

]]> 1.0000000 1.0000000 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»s«/mi»«mn»1«/mn»«/math»

]]> Răspuns corect!

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»s«/mi»«mn»2«/mn»«/math»

]]> Răspuns incorect!

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»s«/mi»«mn»3«/mn»«mspace linebreak=¨newline¨/»«/math»

]]> Răspuns incorect!

]]> Suma matricelor

]]> Răspuns corect!

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»s«/mi»«mn»2«/mn»«/math»

]]> Răspuns incorect!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>m</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raspuns1</mi><mo>=</mo><mi>M</mi><mo>-</mo><msup><mi>N</mi><mo>T</mo></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raspuns2</mi><mo>=</mo><mi>M</mi><mo>+</mo><mi>N</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raspuns3</mi><mo>=</mo><mi>M</mi><mo>+</mo><msup><mi>N</mi><mo>T</mo></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> suma patratelor Fie matricele A=#A şi B=#B.

Atunci A²+B²=#suma

]]> 1.0000000 1.0000000 0 Adevărat Raspuns corect!

]]> Fals Ai calculat greşit!

Matricea 2A^T+B^T este #operatie.

]]> 1.0000000 1.0000000 0 Adevărat Răspusn corect!

]]> Fals Răspuns incorect!