Question

calcular matriz inversa

Answer 1

Resposta:

$A^{-1}=\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$

Explicação passo-a-passo:

A matriz inversa de uma matriz

$X=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

é dada por,

$X^{-1}=\dfrac{1}{ad-bc}\cdot\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]$

Então, para

$A=\left[\begin{array}{ccc}3&5\\4&7\end{array}\right]$

Temos,

$A^{-1}=\dfrac{1}{(3\cdot7)-(4\cdot5)}\cdot\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$

$A^{-1}=\dfrac{1}{21-20}\cdot\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$

$A^{-1}=\dfrac{1}{1}\cdot\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$

$A^{-1}=1\cdot\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$

$A^{-1}=\left[\begin{array}{ccc}7&-5\\-4&3\end{array}\right]$