Question

Dadas as matrizes A= [-4 3 1 2] e B= [1 0 -1 3], calcule o determinante da matriz 3A * 4B e marque a alternativa que contém esse valor

Answer 1

Matriz A:
$3. \left[\begin{array}{ccc}-4&3\\1&2\\\end{array}\right] = \left[\begin{array}{ccc}-12&9\\3&6\\\end{array}\right]$

Matriz B:
$4. \left[\begin{array}{ccc}1&0\\-1&3\\\end{array}\right] = \left[\begin{array}{ccc}4&0\\-4&12\\\end{array}\right]$

Multiplicando as duas:
$\left[\begin{array}{ccc}-12&9\\3&6\\\end{array}\right] . \left[\begin{array}{ccc}4&0\\-4&12\\\end{array}\right] = \left[\begin{array}{ccc}-12 . 4 + 9 . (-4)&-12 . 0 + 9 . 12\\3 . 4 + 6 . (-4)&3 . 0 + 6 . 12\\\end{array}\right]$

$\left[\begin{array}{ccc}-48 - 36&0 + 108\\12 - 24&0 + 72\\\end{array}\right] = \left[\begin{array}{ccc}-84&108\\-12&72\\\end{array}\right]$

-84 . 72 - (-12 . 108) → -6018 - (-1296) → -6018 + 1296 → Determinante: -4752