Question

Dada a matriz:
A= (-2 3)
(-1 2)
Calcule a sua inversa A-¹

Answer 1

Resposta:

$\left[\begin{array}{cc}-2&3\\-1&2\end{array}\right]$

Explicação passo-a-passo:

Seja X a matriz inversa

$\left[\begin{array}{cc}-2&3\\-1&2\end{array}\right]*\left[\begin{array}{cc}a&b\\c&d\end{array}\right] =\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\\\left[\begin{array}{cc}(-2a+3c)&(-2b+3d)\\(-a+2c)&(-b+2d)\end{array}\right]=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\\-2a+3c=1\\-a+2c=0\\a=2c\\subt.\,na\,I\\-2(2c)+3c=1\\-4c+3c=1\\-c=1*(-1)\\c=-1\\como\,\,a=2*c=>-2\\-2b+3d=0*(-1)\\-b+2d=1  *(2)\\\\2b-3d=0\\-2b+4d=2\\\\d=2\\\\\\como\\-b+2d=1 \\-b+2*2=1\\4-1=b\\b=3$

Portanto a matriz A-1

$\left[\begin{array}{cc}-2&3\\-1&2\end{array}\right]$