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Donades les matrius <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mi»#A«/mi»«/math»</span> i <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mi»#B«/mi»«/math»</span>, determinar la matriu X sabent que A·X + B = A.<br /><br /><span style="text-decoration: underline;">NOTACIÓ</span> de la resposta: introdueix directament la matriu (sense escriure "X =") a partir de l'opció de "Copia resposta" o usant l'eina Matrius de l'editor. <br />
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Es compleix que A·X + B= A, cal aïllar X. <br />Primer restem B a ambdós termes de l'equació AX + B - B = A - B i obtenim que AX = A - B.<br />Usarem ara que A<sup>-1</sup>·A = I i multiplicarem ambdós termes de l'equació per A<sup>-1</sup>. Tenim que A<sup>-1</sup>·A·X = A<sup>-1</sup>(A - B) i, per tant, I · X = A<sup>-1</sup>(A - B). <br />Com que I és la matriu identitat es compleix que I · X = X i, per tant, tenim que X = A<sup>-1</sup>·(A - B). Realitzant aquests càlculs correctament, obtenim la matriu X. <br /><br /><br />
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Yes, case must match
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Answer 1
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Molt bé.
Answer 2
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Atenció, has de tenir present que el producte de matrius no compleix la propietat commutativa i, llavors, no és el mateix X =(A - B)· A<sup>-1</sup>que X = A<sup>-1</sup>·(A - B). <br />
Answer 3
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None
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83.33333%
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66.66667%
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33.33333%
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16.66667%
14.28571%
12.5%
11.11111%
10%
5%
Feedback
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33.33333%
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Wednesday, 12 June 2013, 1:03 PM
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Wednesday, 12 June 2013, 1:03 PM
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