Question

calcule a matriz inversa da matriz A = $\left[\begin{array}{ccc}5&-2\\-7&3\\\end{array}\right]$

Answer 1

$\displaystyle \Delta =\left|\begin{matrix} 5&-2\\-7&3 \end{matrix}\right|=(5)(3)-(-7)(-2)=1$

Matriz de cofactores
$\displaystyle C_{11} =(-1)^{1+1}(3)=3\hspace{1cm} C_{12} =(-1)^{1+2}(-2)=2\\ \\ C_{21} =(-1)^{2+1}(-7)=7\hspace{1cm} C_{22} =(-1)^{2+2}(5)=5\\ \\ \\ A^{-1}=\frac{\left[\begin{matrix}C_{11}&C_{12}\\ C_{21}&C_{22}\end{matrix}\right]}{\Delta}\\ \\ \\ \boxed{A^{-1}=\left[\begin{matrix}3&2\\ 7&5\end{matrix}\right]}$