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Test-Lidia
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Dadas las matrices A = #A y B = #B, determinar la matriz X sabiendo que A·X + B = A.<br /><br /><br /><span style="text-decoration: underline;">NOTACIÓN</span> de la respuesta: introduce directamente la matriz (sin escribir "X =") a partir de la opción de "Copia respuesta" o usando la herramienta Matrices del editor.<br />
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Se cumple que A·X + B= A, se debe hallar X. <br />Primero restamos B a ambos términos de la ecuación AX + B - B = A - B y obtenemos que AX = A - B.<br />Usaremos ahora que A<sup>-1</sup>·A = I y multiplicaremos ambos términos de la ecuación por A<sup>-1</sup>. Tenemos que A<sup>-1</sup>·A·X = A<sup>-1</sup>(A - B) y, por tanto, I · X = A<sup>-1</sup>(A - B). <br />Como I es la matriz identidad se cumple que I · X = X y, entonces, tenemos que X = A<sup>-1</sup>·(A - B). Realitzando estos cálculos correctamente, obtenemos la matriz X. <br /><br /><br />
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Answer 1
Answer
Grade
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83.33333%
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Molt bé.
Answer 2
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83.33333%
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66.66667%
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33.33333%
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Atención, debes tener en cuenta que el producto de matrices no cumple la propiedad conmutativa y, entonces, no es el mismo X =(A - B)· A<sup>-1</sup>que X = A<sup>-1</sup>·(A - B). <br />
Answer 3
Answer
Grade
None
100%
90%
83.33333%
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75%
70%
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, 1:11 PM
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Wednesday, 12 June 2013, 1:11 PM
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