Respuesta :
Explicación paso a paso:
Matriz inversa de
[tex]|A|= \left[\begin{array}{ccc}1&0&1\\3&2&1\\7&6&5\end{array}\right][/tex]
Hallamos el determinante de la matriz:
[tex]|A|= \left[\begin{array}{ccc}1&0&1\\3&2&1\\7&6&5\end{array}\right] \\\\\\ |A|= (1)(2)(5)+(3)(6)(1)+(7)(0)(1)-(7)(2)(1)-(1)(6)(1)-(3)(0)(5) \\\\ |A|= 10+18+0-14-6+0 \\\\ |A|= 8[/tex]
Hallamos la matriz adjunta transpuesta:
[tex]A = \left[\begin{array}{ccc}1&0&1\\3&2&1\\7&6&5\end{array}\right] \\\\\\ adj(A) = \left[\begin{array}{ccc}4&-8&4\\6&-2&-6\\-2&2&2\end{array}\right] \\\\\\adj(A^{T}) = \left[\begin{array}{ccc}4&6&-2\\-8&-2&2\\4&-6&2\end{array}\right][/tex]
Hallamos la inversa de la matriz:
[tex]A^{-1} = \frac{1}{|A|}. Adj(A^{T}) \\\\\\ A^{-1} = \frac{1}{|8|}.\left[\begin{array}{ccc}4&6&-2\\-8&-2&2\\4&-6&2\end{array}\right] \\\\\\ A^{-1} = \left[\begin{array}{ccc}0.5&0.75&-0.25\\-1&-0.25&0.25\\0.5&-0.75&0.25\end{array}\right][/tex]