Question

A matriz inversa de M =
2 -3 O
1 2 - 1
- 1 0 1
é:

Answer 1

$\boxed{\begin{array}{l}\sf M=\begin{pmatrix}\sf2&\sf-3&\sf0\\\sf1&\sf2&\sf-1\\\sf-1&\sf0&\sf1\end{pmatrix}\\\sf det~M=2\cdot2+3(1-1)+0(0+2)=4\\\sf adj~M=\begin{pmatrix}\sf2&\sf3&\sf3\\\sf0&\sf2&\sf2\\\sf2&\sf3&\sf7\end{pmatrix}\\\sf M^{-1}=\dfrac{1}{det~M}\cdot adj~M\\\sf M^{-1}=\dfrac{1}{4}\cdot\begin{pmatrix}\sf2&\sf3&\sf3\\\sf0&\sf2&\sf2\\\sf2&\sf3&\sf7\end{pmatrix}\end{array}}$