Question

1. Calcular A-B+2C, sendo dadas:
A = [ 0 0 2
0 −4 15
], B = [1 0 3
−1 2 5] e C = [2 1 3 1 −1 −6]

Answer 1

Resposta:

Temos,

$A=\left[\begin{array}{ccc}0&0&2\\0&-4&15\end{array}\right]$

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

$C=\left[\begin{array}{ccc}2&1&3\\1&-1&-6\end{array}\right]$

Para o cálculo de $A-B+2C$,

$\left[\begin{array}{ccc}0&0&2\\0&-4&15\end{array}\right]-\left[\begin{array}{ccc}1&0&3\\-1&2&5\end{array}\right]+2\cdot\left[\begin{array}{ccc}2&1&3\\1&-1&-6\end{array}\right]=$

$\left[\begin{array}{ccc}0&0&2\\0&-4&15\end{array}\right]-\left[\begin{array}{ccc}1&0&3\\-1&2&5\end{array}\right]+\left[\begin{array}{ccc}2\cdot2&2\cdot1&2\cdot3\\2\cdot1&2\cdot(-1)&2\cdot(-6)\end{array}\right]=$

$\left[\begin{array}{ccc}0&0&2\\0&-4&15\end{array}\right]-\left[\begin{array}{ccc}1&0&3\\-1&2&5\end{array}\right]+\left[\begin{array}{ccc}4&2&6\\2&-2&-12\end{array}\right]=$

$\left[\begin{array}{ccc}0-1+4&0-0+2&2-3+6\\0+1+2&-4-2-2&15-5-12\end{array}\right]=$

$\left[\begin{array}{ccc}3&2&5\\3&-8&-2\end{array}\right]$