Question

Determine a inversa da matriz A.
A= (2 1)
(5 3)

Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

$A = \large\mathsf{\begin{vmatrix}2&1\\5&3\end{vmatrix}}$

$\boxed{\boxed{A.A^{-1} = I}}$

$\large\mathsf{\begin{vmatrix}2&1\\5&3\end{vmatrix}}.\large\mathsf{\begin{vmatrix}a&b\\c&d\end{vmatrix}} = \large\mathsf{\begin{vmatrix}1&0\\0&1\end{vmatrix}}$

$\begin{cases}2a + c = 1\: (-3)\\5a + 3c = 0\\2b + d = 0\: (-3)\\5b + 3d = 1\end{cases}$

$\begin{cases}-6a - 3c = -3\\5a + 3c = 0\\-6b - 3d = 0\\5b + 3d = 1\end{cases}$

$\boxed{\boxed{a = 3}}$

$\boxed{\boxed{b = -1}}$

$\boxed{\boxed{c = -5}}$

$\boxed{\boxed{d = 2}}$

$A^{-1} = \large\mathsf{\begin{vmatrix}3&-1\\-5&2\end{vmatrix}}$