Question

Qual é a matriz inversa de
A = | 1 2 | ?
| 0 -3 |​

Answer 1

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$\sf A=\begin{vmatrix}\sf{1}&\sf{2}\\\sf{0}&\sf{-3}\end{vmatrix}\\\sf det~A=-3\\\sf cof~A=\begin{vmatrix}\sf{-3}&\sf{0}\\\sf{-2}&\sf{1}\end{vmatrix}\\\sf Adj~A=(cof~A)^T\\\sf Adj~A=\begin{vmatrix}\sf{-3}&\sf{-2}\\\sf{0}&\sf{1}\end{vmatrix}$

$\sf A^{-1}=\dfrac{1}{det~A}\cdot Adj~A\\\sf A^{-1}=-\dfrac{1}{3}\cdot\begin{vmatrix}\sf{-3}&\sf{-2}\\\sf{0}&\sf{1}\end{vmatrix}=\begin{vmatrix}\sf{1} &\sf{\dfrac{2}{3}}\\\sf{0}&\sf{-\dfrac{1}{3}}\end{vmatrix}$