Question

Calcule o determinante das matrizes dadas:

A) {1 -5 / 2 1}
B) { -8}
C) {2 0 2 / 3 4 3 / 1 7 -1}
D) {1 3 2 / 1 2 1 / 5 12 1}

Answer 1

A)
$\left[\begin{array}{cc}1&-5\\2&1\end{array}\right]$
det = (1.1) - (2.-5)
det = 1 + 10
det = 11

B)
det = -8

C) Usando a regra de Sarrus:
$\left[\begin{array}{ccccc}2&0&2&2&0\\3&4&3&3&4\\1&7&-1&1&7\end{array}\right]$
→ (2.4.-1) + (0.3.1) + (2.3.7) → -8 + 42 → 34
→ (0.3.-1) + (2.3.7) + (2.4.1) → 42 + 8 → 50
det = 34 - 50 = -16

D) Usando a regra de Sarrus:
$\left[\begin{array}{ccccc}1&3&2&1&3\\1&2&1&1&2\\5&12&1&5&12\end{array}\right]$
→ (1.2.1) + (3.1.5) + (2.1.12) → 2 + 15 + 24 → 41
→ (3.1.1) + (1.1.12) + (2.2.5) → 3 + 12 + 20 → 35
det = 41 - 35 = 6