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Question text
Sigui A la matriu associada d'un sistema que té dimensió #n x #n i A* és la matriu ampliada d'aquest sistema. Marca les afirmacions que són certes:
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a., b., c., ...
A., B., C., ...
1., 2., 3., ...
i., ii., iii., ...
I., II., III., ...
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Algorithm
Choice 1
Answer
es tracta d'un sistema de #n equacions amb #n incògnites
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83.33333%
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Feedback
Molt bé
Choice 2
Answer
la dimensió de la matriu ampliada és #m x #n
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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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Feedback
Atenció, estem afegint una columna a la matriu A, no una fila.
Choice 3
Answer
la dimensió de la matriu ampliada és #n x #m
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
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20%
16.66667%
14.28571%
12.5%
11.11111%
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5%
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-12.5%
-14.28571%
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Feedback
Molt bé, estem afegint una columna a la matriu A.
Choice 4
Answer
Si el rang d'A és igual a #n, llavors ja podem afirmar que el rang de la matriu ampliada és #n
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
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33.33333%
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16.66667%
14.28571%
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11.11111%
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Feedback
Molt bé. Els menors d'A<sup>*</sup> d'ordre més gran que podem construir tenen dimensió #n x #n, per tant, el rang màxim d'A<sup>*</sup> és #n. Si A té rang #n vol dir que <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfenced close="|" open="|"»«mi»A«/mi»«/mfenced»«mo»§#8800;«/mo»«mn»0«/mn»«/math»</span> i, per tant, A<sup>*</sup> té un menor d'ordre #n amb determinant diferent de 0.
Choice 5
Answer
Si el rang d'A és menor que #n, llavors ja podem afirmar que el rang de la matriu ampliada és menor que #n
Grade
None
100%
90%
83.33333%
80%
75%
70%
66.66667%
60%
50%
40%
33.33333%
30%
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16.66667%
14.28571%
12.5%
11.11111%
10%
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Feedback
Fixa't que el rang de la matriu ampliada encara pot ser #n, malgrat que el rang d'A no ho sigui. Si un menor format per columnes d'A i la nova columna d' A<sup>* </sup> té determinant diferent de 0, llavors el rang de l'ampliada serà #n. Per exemple, considera <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»A«/mi»«mo»*«/mo»«mo»=«/mo»«mi»#Aamp«/mi»«/math»</span>.<br />
Choice 6
Answer
Grade
None
100%
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83.33333%
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66.66667%
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33.33333%
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Feedback
Choice 7
Answer
Grade
None
100%
90%
83.33333%
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70%
66.66667%
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33.33333%
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Feedback
Choice 8
Answer
Grade
None
100%
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83.33333%
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70%
66.66667%
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33.33333%
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Feedback
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For any partially correct response
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Penalty for each incorrect try
100%
50%
33.33333%
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0%
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Created
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on
Wednesday, 12 June 2013, 1:03 PM
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on
Wednesday, 12 June 2013, 1:03 PM
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