Question

Calcule a soma entre as matrizes A(aij)2x2em que aij=i+j e B(bij)2x2 tal que bij=
(i+j) elevado a 2​

Answer 1

Resposta:

A + B = $\left[\begin{array}{ccc}6&12\\12&20\end{array}\right]$

Explicação passo-a-passo:

Seja a matriz A = $\left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]$, com aij = i + j e B =$\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]$, com bij = (i + j)², então:

A = $\left[\begin{array}{ccc}1+1&1+2\\2+1&2+2\end{array}\right]$ = $\left[\begin{array}{ccc}2&3\\3&4\end{array}\right]$

B = $\left[\begin{array}{ccc}(1+1)^2&(1+2)^2\\(2+1)^2&(2+2)^2\end{array}\right]$ = $\left[\begin{array}{ccc}4&9\\9&16\end{array}\right]$

Logo,

A + B = $\left[\begin{array}{ccc}2+4&3+9\\9+3&4+16\end{array}\right]$ = $\left[\begin{array}{ccc}6&12\\12&20\end{array}\right]$ .