Question

Matrizes Sendo A$\left[\begin{array}{ccc}-2&2&\\&&\\-3&3&\end{array}\right] e B= \left[\begin{array}{ccc}5&-1&\\3&4&\\&&\end{array}\right] ,$


MAtriz x tal que 3x-2a= b é:

Answer 1

Resposta:

Explicação passo-a-passo:

$A=\left[\begin{array}{cc}-2&2\\-3&3\end{array}\right]\\\\\\2A=\left[\begin{array}{cc}-2.2&2.2\\-3.2&3.2\end{array}\right]\\\\\\2A=\left[\begin{array}{cc}-4&4\\-6&6\end{array}\right]$

$B=\left[\begin{array}{cc}5&-1\\3&4\end{array}\right]$

Queremos a matriz X tal que:

3X-2A=B

3X=B+2A

$B+2A=\left[\begin{array}{cc}5&-1\\3&4\end{array}\right]+\left[\begin{array}{cc}-4&4\\-6&6\end{array}\right]\\\\\\B+2A=\left[\begin{array}{cc}5-4&-1+4\\3-6&4+6\end{array}\right]\\\\\\B+2A=\left[\begin{array}{cc}1&3\\-3&10\end{array}\right]$

$3X=B+2A\\\\\\3X=\left[\begin{array}{cc}1&3\\-3&10\end{array}\right]\\\\\\X=\frac{1}{3}\left[\begin{array}{cc}1&3\\-3&10\end{array}\right]\\\\\\X=\left[\begin{array}{cc}1.\frac{1}{3} &3.\frac{1}{3} \\-3.\frac{1}{3} &10.\frac{1}{3} \\\end{array}\right]\\\\\\\\X=\left[\begin{array}{cc}\frac{1}{3} &1\\-1&\frac{10}{3}\end{array}\right]$

Opção 2