Question

Determine a matriz X + Y tais que X - Y (segue a imagem) e X + Y = (segue a imagem)

Answer 1

Resposta:

Explicação passo a passo:

$X+Y=\left[\begin{array}{ccc}0&1\\-6&4\end{array}\right] (I)\\\\\\X-Y=\left[\begin{array}{ccc}2&-7\\4&6\end{array}\right] (II)$

Para resolver faça (I)+(II):

$\displaystyle X+X+Y+Y=\left[\begin{array}{ccc}0+2&1-7\\-6+4&4+6\end{array}\right] \\\\\\2X=\left[\begin{array}{ccc}2&-6\\-2&10\end{array}\right] \\\\\\\\X=\left[\begin{array}{ccc}\frac{2}{2} &\frac{-6}{2}\\-\frac{2}{2}&\frac{10}{2}\end{array}\right] \\\\\\\\X=\left[\begin{array}{ccc}1 &-3\\-1&5\end{array}\right]$

Substituindo X em (I)

$\left[\begin{array}{ccc}1 &-3\\-1&5\end{array}\right]+Y=\left[\begin{array}{ccc}0&1\\-6&4\end{array}\right]\\\\\\Y = \left[\begin{array}{ccc}0&1\\-6&4\end{array}\right]-\left[\begin{array}{ccc}1 &-3\\-1&5\end{array}\right]\\\\\\Y=\left[\begin{array}{ccc}0-1 &1-(-3)\\-6+1&4-5\end{array}\right]\\\\\\Y=\left[\begin{array}{ccc}-1 &4\\-5&-1\end{array}\right]$