Question

Dados as matrizes : A = [1 3 ] , B = [-1 5] , e C = [ 4 0] .
2 -4 0 6 -5 2
Calcule:
a) A + B
b) B+ C
c) A-C
d) B-C
e) A+B-C

Obs: Quero todos os cálculos, passo a passo, por favor!

Answer 1

Vamos precisar fazer a soma e a subtração das matrizes. Para somar ou subtrair, basta realizar a operação de cada posição com cada posição:

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

b) B+C
$\left[\begin{array}{ccc}-1&5\\0&6\end{array}\right]$ + $\left[\begin{array}{ccc}4&0\\-5&2\end{array}\right]$ 
$\left[\begin{array}{ccc}-1+4&5+0\\0-5&6+2\end{array}\right]$
$\left[\begin{array}{ccc}3&5\\-5&8\end{array}\right]$

c) A-B (considerei o que esta escrito na imagem)
$\left[\begin{array}{ccc}1&3\\2&-4\end{array}\right]$ - $\left[\begin{array}{ccc}-1&5\\0&6\end{array}\right]$
$\left[\begin{array}{ccc}1-(-1)&3-5\\2-0&-4-6\end{array}\right]$ 
$\left[\begin{array}{ccc}2&-2\\2&-10\end{array}\right]$ 

d) B-C
$\left[\begin{array}{ccc}-1&5\\0&6\end{array}\right]$ - $\left[\begin{array}{ccc}4&0\\-5&2\end{array}\right]$ 
$\left[\begin{array}{ccc}-1-4&5-0\\0-(-5)&6-2\end{array}\right]$
$\left[\begin{array}{ccc}-5&5\\5&4\end{array}\right]$

e) A+B-C
$\left[\begin{array}{ccc}1&3\\2&-4\end{array}\right]$ + $\left[\begin{array}{ccc}-1&5\\0&6\end{array}\right]$ - $\left[\begin{array}{ccc}4&0\\-5&2\end{array}\right]$ 
Como já sabemos quanto é A+B: $\left[\begin{array}{ccc}0&8\\2&2\end{array}\right]$, vamos apenas subtrair C:
$\left[\begin{array}{ccc}0-4&8-0\\2-(-5)&2-2\end{array}\right]$
$\left[\begin{array}{ccc}-4&8\\7&0\end{array}\right]$