Question

Determine, se existir, a inversa de A = [1 3]
[02]

Answer 1

$\left[\begin{array}{ccc}1&3\\0&2\end{array}\right]$

Uma matriz inversa só vai existirse, e somente se:

$A$ × $A^{-1} = In$ (matriz identidade)

Logo:

$\left[\begin{array}{ccc}1&3\\0&2\end{array}\right]$ × $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ = $\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]$

Logo:

1 × a = 1   a=1
3 × b = 0   b=0
0 x c = 0   c=0
2 × d = 1   d=0,5 ou $\frac{1}{2}$

$A^{-1}= \left[\begin{array}{ccc}1&0\\0& \frac{1}{2} \end{array}\right]$