Question

Sejam as matrizes
A= 1 2 3
4 5 6
7 8 9

B= -1 0 3
5 6 8
4 -3 6
Obtenha a matriz X no seguinte caso: X+A= 2B

Answer 1

Em matrizes, as operações de soma, subtração e multiplicação por escalar (numero) são feitas termo a termo.

$X+A=2B$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] \;+\;\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] =2\;.\;\left[\begin{array}{ccc}-1&0&3\\5&6&8\\4&-3&6\end{array}\right]$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] \;+\;\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] =\left[\begin{array}{ccc}2\,.\,-1&2\,.\,0&2\,.\,3\\2\,.\,5&2\,.\,6&2\,.\,8\\2\,.\,4&2\,.\,-3&2\,.\,6\end{array}\right]$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] \;+\;\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] =\left[\begin{array}{ccc}-2&0&6\\10&12&16\\8&-6&12\end{array}\right]$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] =\left[\begin{array}{ccc}-2&0&6\\10&12&16\\8&-6&12\end{array}\right]\;-\;\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] =\left[\begin{array}{ccc}-2-1&0-2&6-3\\10-4&12-5&16-6\\8-7&-6-8&12-9\end{array}\right]$

$\left[\begin{array}{ccc}x_{_{11}}&x_{_{12}}&x_{_{13}}\\x_{_{21}}&x_{_{22}}&x_{_{23}}\\x_{_{31}}&x_{_{32}}&x_{_{33}}\end{array}\right] \;=\;X\;=\;\left[\begin{array}{ccc}-3&-2&3\\6&7&10\\1&-14&3\end{array}\right]$