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En los problemas 1y2 compruebe que la matriz B es la inversa de la matriz A​?

En los problemas 1y2 compruebe que la matriz B es la inversa de la matriz A​.

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1. <img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%2F2%5C%5C2%263%2F2%5Cend%7Barray%7D%5Cright%5D%20x%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-1%5C%5C-4%262%5Cend%7Barray%7D%5Cright%5D" /><img src="https://tex.z-dn.net/?

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Anapaola8878

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1. <img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%2F2%5C%5C2%263%2F2%5Cend%7Barray%7D%5Cright%5D%20x%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-1%5C%5C-4%262%5Cend%7Barray%7D%5Cright%5D" /><img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1x3-4x%281%2F2%29%261x-1%2B2x%281%2F2%29%5C%5C2x3-%283%2F2%29x-4%29%262x-1%2B%283%2F2%29x2%5Cend%7Barray%7D%5Cright%5D" /><img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D" />2.

<img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%260%5C%5C3%260%262%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20x%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%262%5C%5C1%26-1%262%5C%5C-3%262%26-3%5Cend%7Barray%7D%5Cright%5D%20%3D%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.2-1.1%2B0.-3%261.-1-1.-1%2B0.2%261.2-1.2%2B0.-3%5C%5C3.2%2B0.1%2B2.-3%263.-1%2B0.-1%2B2.2%263.2%2B0.2%2B2.-3%5C%5C1.2%2B1.1%2B1.-3%261.-1%2B1.-1%2B1.2%261.2%2B1.2%2B1.-3%5Cend%7Barray%7D%5Cright%5D%20%3D%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D" />Como ves, en ambos casos dan la matriz identidad (es la que en la diagonal tiene 1 y el resto es 0), entonces A es la inversa de B y B a su vez es la inversa de A.