*&@#URGENTE*&@#
Determine se A é inversível e, se for, encontre sua inversa.
a) A=![a)\left[\begin{array}{ccc}1&0&1\\1&1&0\\0&1&1\end{array}\right] \\b)\left[\begin{array}{ccc}1&1&1\\1&0&0\\0&1&1\end{array}\right] \\c)\left[\begin{array}{ccc}0&0&1\\1&1&0\\-1&1&1\end{array}\right]](https://tex.z-dn.net/?f=a%29%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%26amp%3B1%5C%5C1%26amp%3B1%26amp%3B0%5C%5C0%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5C%5Cb%29%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B1%26amp%3B1%5C%5C1%26amp%3B0%26amp%3B0%5C%5C0%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5C%5Cc%29%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3B0%26amp%3B1%5C%5C1%26amp%3B1%26amp%3B0%5C%5C-1%26amp%3B1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D "a)\left[\begin{array}{ccc}1&0&1\\1&1&0\\0&1&1\end{array}\right] \\b)\left[\begin{array}{ccc}1&1&1\\1&0&0\\0&1&1\end{array}\right] \\c)\left[\begin{array}{ccc}0&0&1\\1&1&0\\-1&1&1\end{array}\right]")
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Explicação passo-a-passo:
matriz A
1 0 1
1 1 0
0 1 1
det = 2
matriz B
1 1 1
1 0 0
0 1 1
det = 0
matriz C
0 0 1
1 1 0
-1 1 1
det = 2
A e C sao inversíveis
A^-1 =
1/2 1/2 -1/2
-1/2 1/2 1/2
1/2 -1/2 1/2
C^-1 =
1/2 1/2 -1/2
-1/2 1/2 1/2
1 0 0
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