Question

São dadas as matrizes A = (aij) e B = (bij), quadradas de ordem 2, com aij = 3i + 4j e bij = – 4i – 3j. Considerando C = A + B, calcule a soma da diagonal principal da matriz C.

Answer 1

$A =(aij)_{2x2}$            aij = 3i + 4j
a11 → 3 . 1 + 4 . 1 → 3 + 4 → 7           a12 → 3 . 1 + 4 . 2 → 3 + 8 → 11
a21 → 3 . 2 + 4 .1 → 6 + 4 → 10        a22 → 3 . 2 + 4 . 2 → 6 + 8 → 14

Matriz A:
$\left[\begin{array}{ccc}7&11\\10&14\\\end{array}\right]$

$B =(bij)_{2x2}$            bij = – 4i – 3j
a11 → -4 . 1 - 3 . 1 → -4 - 3 → -7         a12 → -4 . 1 - 3 . 2 → -4 - 6 → -10
a21 → -4 . 2 - 3 . 1 → -8 - 3 → -11      a22 → -4 . 2 - 3 . 2 → -8 - 6 → -14

Matriz B:
$\left[\begin{array}{ccc}-7&-10\\-11&-14\\\end{array}\right]$

Calculando a Matriz C que é igual a A + B:
$\left[\begin{array}{ccc}7&11\\10&14\\\end{array}\right] + \left[\begin{array}{ccc}-7&-10\\-11&-14\\\end{array}\right] = \left[\begin{array}{ccc}0&1\\-1&0\\\end{array}\right]$

A soma da diagonal principal de C: 0 + 0 = 0