Question

Calcule a inversa de:​

Answer 1

Teorema da matriz inversa

$\boxed{\boxed{\mathsf{{A}^{-1}=\dfrac{1}{det\,A}.adj\,A}}}$

$A=\begin{pmatrix}0&4\\-1&2\end{pmatrix}$

$det\,A=0.2-(-1.4)=4$

$cof\,A=\begin{pmatrix}2&1\\-4&0\end{pmatrix}$

$adj\,A={(cof\,A)}^{T}=\begin{pmatrix}2&-4\\1&0\end{pmatrix}$

${A}^{-1}=\dfrac{1}{4}.\begin{pmatrix}2&-4\\1&0\end{pmatrix} = \begin{pmatrix} \dfrac{1}{2} &-1\\ \dfrac{1}{4} &0\end{pmatrix}$