Question

a) Sejam as matrizes A = 1 2 3 e B= - 1 0 2 obtenha a matriz X no seguinte caso X + A = 2b
4 5 6 5 6 8
7 8 9 4 -3 6

Answer 1

Olá

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Aplicando as propriedades de matrizes

$X+A=2B \\ \\ X+A-A=2B-A \\ \\\boxed{ X=2B-A}$

$A= \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ B= \left[\begin{array}{ccc}-1&0&2\\5&6&8\\4&-3&6\end{array}\right]$


Para encontrar a matriz "2b", basta multiplicar cada elemento da matriz por 2.

$2B= \left[\begin{array}{ccc}-1\cdot(2)&0\cdot(2)&2\cdot(2)\\5\cdot(2)&6\cdot(2)&8\cdot(2)\\4\cdot(2)&-3\cdot(2)&6\cdot(2)\end{array}\right] \\ \\ \\ \\ \boxed{2B= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}$


Agora que já temos a matriz "2b", basta subtrair (2b - A)

$X=2B-A \\ \\ X= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}~~~~~~-~~~~~~\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ X= \left[\begin{array}{ccc}(-2-1)&(0-2)&(4-3)\\(10-4)&(12-5)&(16-6)\\(8-7)&(-6-8)&(12-9)\end{array}\right] \\ \\ \\ \\ \boxed{\boxed{X= \left[\begin{array}{ccc}-3&-2&1\\6&7&10\\1&-14&3\end{array}\right] }}$