Question

Matrizes.

Se A = ( 1 -2 3 | 4 0 5 ) e B = ( 6 -1 -8 | 0 2 -1) determine:


a) $\frac{-2}{3}$A + 3B.

b) Calcule x e y considerando as matrizes A e B acima $\left \{ {{x + 2y = 3A + B} \atop {x - y = A - 5B}} \right.$.

Answer 1

Oi! Tá tudo bem contigo?

Façamos da seguinte forma:

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

$\displaystyle -\frac{2}{3}A+3B= -\frac{2}{3}\left[\begin{array}{ccc}1&-2&3\\4&0&5\end{array}\right]+3\left[\begin{array}{ccc}6&-1&-8\\0&2&-1\end{array}\right] \\ \\ \\ =\left[\begin{array}{ccc}- \frac{2}{3} & \frac{4}{3} &-2\\ -\frac{8}{3} &0&- \frac{10}{3} \end{array}\right] + \left[\begin{array}{ccc}18&-3&-24\\0&6&-3\end{array}\right]$

$= \left[\begin{array}{ccc}- \frac{2}{3}+18 & \frac{4}{3}-3 &-2-24\\ -\frac{8}{3}+0 &0+6&- \frac{10}{3}-3 \end{array}\right] = \left[\begin{array}{ccc} \frac{52}{3} & -\frac{5}{3} &-26\\ -\frac{8}{3} &6&- \frac{19}{3} \end{array}\right]$