Question

Dadas as matrizes A=[1 −3 0 4 ] , B=[−2 1 0 −3] e C=[−1 −2 −3 0 ] calcule a matriz X tal que X+2C=A+3B.

Answer 1

x = $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

X + 2C = A+3B equivale:

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]+ \left[\begin{array}{ccc}-2&-4\\-6&0\end{array}\right]= \left[\begin{array}{ccc}1&-3\\0&4\end{array}\right] + \left[\begin{array}{ccc}-6&3\\0&-9\end{array}\right]$

Fazendo as somas das matrizes, vai ficar

a - 2 = -5 -> a = -3
b - 4 = 0 -> b = 4
c - 6 = 0 -> c = 6
d = -5 

Logo a matriz X será:

$\left[\begin{array}{ccc}-3&4\\6&-5\end{array}\right]$