Question

resolva a equação matricial [-7...2...1] +2X = [11...0...3]

Answer 1

$\left[\begin{array}{ccc}-7&2&1\end{array}\right] +2X= \left[\begin{array}{ccc}11&0&3\end{array}\right]$
vamos considerar que
$X=\left[\begin{array}{ccc}x&y&z\end{array}\right] \implies 2X=\left[\begin{array}{ccc}2x&2y&2z\end{array}\right]$
montamos a seguinte relação:
$\displaystyle i)~~~~\left[\begin{array}{ccc}-7&2&1\end{array}\right] +2X= \left[\begin{array}{ccc}11&0&3\end{array}\right] \\\\ii)~~~\left[\begin{array}{ccc}-7&2&1\end{array}\right] +\left[\begin{array}{ccc}2x&2y&2z\end{array}\right]= \left[\begin{array}{ccc}11&0&3\end{array}\right] \\\\iii)~~\left[\begin{array}{ccc}2x-7&2y+2&2z+1\end{array}\right]= \left[\begin{array}{ccc}11&0&3\end{array}\right]\\\\iv)~~2x-7=11\implies x=\frac{18}{2}=\boxed9\\\\v)~~~2y+2=0\implies y=\frac{-2}{2}=\boxed{-1}\\\\vi)~~2z+1=3\implies z=\frac{2}{2}=\boxed{1}$
Ou seja:
$X= \left[\begin{array}{ccc}9&-1&1\end{array}\right]$
para comprovar fazemos:
$2X= \left[\begin{array}{ccc}18&-2&2\end{array}\right] \\\\ \left[\begin{array}{ccc}-7&2&1\end{array}\right] +2X= \left[\begin{array}{ccc}-7&2&1\end{array}\right] +\left[\begin{array}{ccc}18&-2&2\end{array}\right] \\\\ \left[\begin{array}{ccc}(-7+18)&(2-2)&(1+2)\end{array}\right]=\boxed{\left[\begin{array}{ccc}11&0&3\end{array}\right] }$