Question

Sejam as matrizes A= $\left[\begin{array}{ccc}2&3\\1&4\end{array}\right]$ e B= $\left[\begin{array}{ccc}4&5\\6&7\end{array}\right]$ .Calcule:


a) A.B
B) $A^{2}$ (obs: $A^{2}$ = A.A)


R= a) $\left[\begin{array}{ccc}26&31\\28&33\end{array}\right]$

R= b) $\left[\begin{array}{ccc}7&18\\6&19\end{array}\right]$

Answer 1

$Ola' \\ \\ a)\\ A.B=\begin{bmatrix}2&3 \\ 1&4\end{bmatrix} .\begin{bmatrix}4&5 \\ 6&7\end{bmatrix} \\ \\ \\ A.B=\begin{bmatrix}2(4)+3(6)&2(5)+3(7) \\ 1(4)+4(6)&1(5)+4(7)\end{bmatrix} \\ \\ \\\boxed{ A.B=\begin{bmatrix}26&31 \\ 28&33\end{bmatrix}} \\ \\ ****************************************** \\ b) \\ A\²=A.A \\ \\ \begin{bmatrix}2&3 \\ 1&4\end{bmatrix}.\begin{bmatrix}2&3 \\ 1&4\end{bmatrix} \\ \\ \\ \begin{bmatrix}2(2)+3(1)&2(3)+3(4) \\ 1(2)+4(1)&1(3)+4(4)\end{bmatrix}$

$\boxed{A\²=A.A=\begin{bmatrix}7&18 \\ 6&9\end{bmatrix} }\\ \\ \\ \mathbb{wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww} \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$