Question

determinar a matriz inversa:
{1 3}
{2 2}

Answer 1

$\begin{pmatrix}1&3&|&1&0\\2&2&|&0&1\end{pmatrix}L_2\rightarrow\,L_2-2L_1\\\\\\\begin{pmatrix}1&3&|&1&0\\0&-4&|&-2&1\end{pmatrix}L_2\rightarrow\frac{-1}{4}\cdot\,L_2\\\\\\\begin{pmatrix}1&3&|&1&0\\0&1&|&\frac{1}{2}&-\frac{1}{4}\end{pmatrix}L_1\rightarrow\,L_1-3L_2\\\\\\\begin{pmatrix}1&0&|&-\frac{1}{2}&\frac{3}{4}\\0&1&|&\frac{1}{2}&-\frac{1}{4}\end{pmatrix}$
 
 Do escalonamento acima, tiramos que a inversa da matriz dada no enunciado é $\boxed{\boxed{A^{-1}=\begin{pmatrix}-\frac{1}{2}&\frac{3}{4}\\\frac{1}{2}&-\frac{1}{4}\end{pmatrix}}}$