Question

18. Uma matriz A é antissimétrica se A = -A. O va- lor de a + b + c + x + y + z para que a matriz A= a 2 -3 x-1 b 2y - 4 Z 4 4 C seja antissimétrica é: S- -1 ī s a) 2 b) 1 c) O e) -2 2 Duma matriz detine​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{A = }\begin{bmatrix}\cancel \textsf{a}&\cancel\textsf{2}&\cancel\textsf{-3}\\\cancel \textsf{x - 1}&\cancel \textsf{b}&\cancel \textsf{2y - 4}\\\cancel \textsf{z}&\cancel\textsf{4}&\cancel \textsf{c}\end{bmatrix}$

$\mathsf{A^t = }\begin{bmatrix}\cancel \textsf{a}&\cancel\textsf{x - 1}&\cancel\textsf{z}\\\cancel \textsf{2}&\cancel \textsf{b}&\cancel \textsf{4}\\\cancel \textsf{-3}&\cancel\textsf{2y - 4}&\cancel \textsf{c}\end{bmatrix}$

$\mathsf{-A^t = }\begin{bmatrix}\cancel \textsf{-a}&\cancel\textsf{-x + 1}&\cancel\textsf{-z}\\\cancel \textsf{-2}&\cancel \textsf{-b}&\cancel \textsf{-4}\\\cancel \textsf{3}&\cancel\textsf{-2y + 4}&\cancel \textsf{-c}\end{bmatrix}$

$\mathsf{A = -A^{t}}$

$\mathsf{-x + 1 = 2\rightarrow x = -1}$

$\mathsf{-2y + 4 = 4\rightarrow y = 0}$

$\mathsf{-z = -3 \rightarrow z = 3}$

$\mathsf{a + b + c + x + y + z = 0 + 0 + 0 + (-1) + 0 + 3}$

$\mathsf{a + b + c + x + y + z = 0 + 0 + 0 - 1 + 0 + 3}$

$\boxed{\boxed{\mathsf{a + b + c + x + y + z = 2}}}\leftarrow\textsf{letra A}$