Sendo
A-1 =
0 n
-1/2 3
a matriz inversa de
A=
m -2
1 0
Calcule m+n
Soluções para a tarefa
Respondido por
129
Boa tarde
Devemos ter ; A* A^-1 =I
![\left[\begin{array}{ccc}m&-2\\1&0\end{array}\right] * \left[\begin{array}{ccc}0&n\\- \frac{1}{2} &3\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \\ \left[\begin{array}{ccc}1&m*n-6\\0&n+0\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \\ \left \{ {{m*n-6=0} \atop {n=1}} \right. \Rightarrow m*1-6=0\Rightarrow m=6 \\ \\ \\ m+n=6+1 \Rightarrow \boxed{m+n=7}](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dm%26amp%3B-2%5C%5C1%26amp%3B0%5Cend%7Barray%7D%5Cright%5D+%2A++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26amp%3Bn%5C%5C-+%5Cfrac%7B1%7D%7B2%7D+%26amp%3B3%5Cend%7Barray%7D%5Cright%5D+%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%5C%5C0%26amp%3B1%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C++%5C%5C+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3Bm%2An-6%5C%5C0%26amp%3Bn%2B0%5Cend%7Barray%7D%5Cright%5D+%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B0%5C%5C0%26amp%3B1%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C++%5C%5C++%5Cleft+%5C%7B+%7B%7Bm%2An-6%3D0%7D+%5Catop+%7Bn%3D1%7D%7D+%5Cright.+%5CRightarrow+m%2A1-6%3D0%5CRightarrow+m%3D6+%5C%5C++%5C%5C++%5C%5C+m%2Bn%3D6%2B1+%5CRightarrow+%5Cboxed%7Bm%2Bn%3D7%7D "\left[\begin{array}{ccc}m&-2\\1&0\end{array}\right] * \left[\begin{array}{ccc}0&n\\- \frac{1}{2} &3\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \\ \left[\begin{array}{ccc}1&m*n-6\\0&n+0\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \\ \\ \left \{ {{m*n-6=0} \atop {n=1}} \right. \Rightarrow m*1-6=0\Rightarrow m=6 \\ \\ \\ m+n=6+1 \Rightarrow \boxed{m+n=7}")
Devemos ter ; A* A^-1 =I
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