Question

Dadas as matrizes A = [5, 2, -1, 1], B = [2, -2, 0, 1] e X = [a, b, c, d] tais que 2A - X = B, então, o determinante da matriz X é:
A - 10
B - 15
C - 20
D - 25
E - N.D.A

Answer 1

Resposta:

C) 20

Explicação passo a passo:

$2A-X=B$

$2\left[\begin{array}{cc}5&2\\-1&1\end{array}\right]-\left[\begin{array}{cc}a&b\\c&d\end{array}\right]=\left[\begin{array}{cc}2&-2\\0&1\end{array}\right]$

$\left[\begin{array}{cc}10&4\\-2&2\end{array}\right]-\left[\begin{array}{cc}a&b\\c&d\end{array}\right]=\left[\begin{array}{cc}2&-2\\0&1\end{array}\right]$

→ 10 - a = 2 ∴ a = 8

→ 4 - b = -2 ∴ b = 6

→ -2 - c = 0 ∴ c = -2

→ 2 - d = 1 ∴ d = 1

$X=\left[\begin{array}{cc}8&6\\-2&1\end{array}\right]$

$detX=\left|\begin{array}{cc}8&6\\-2&1\end{array}\right|=8\cdot1-6\cdot(-2)=8+12=20$