Question

77. Dadas as matrizes A e B, calcule o valor de x tal que
det A = -det B.

A= |1 0 x|
|2 1 2|
|-x 3 0|

B= |x 1 0|
|1 -x 2|
|3 0 1 |

POR FAVOR ME AJUDEMMMMM É URGENTEEEE

Answer 1

Explicação passo-a-passo:

$\sf det~(A)=1\cdot1\cdot0+0\cdot2\cdot(-x)+x\cdot2\cdot3-(-x)\cdot1\cdot x-3\cdot2\cdot1-0\cdot2\cdot0$

$\sf det~(A)=0-0+6x+x^2-6-0$

$\sf det~(A)=x^2+6x-6$

$\sf det~(B)=x\cdot(-x)\cdot1+1\cdot2\cdot3+0\cdot1\cdot0-3\cdot(-x)\cdot 0-0\cdot2\cdot x-1\cdot1\cdot1$

$\sf det~(B)=-x^2+6+0+0-0-1$

$\sf det~(B)=-x^2+5$

$\sf det~(A)=-det~(B)$

$\sf x^2+6x-6=-(-x^2+5)$

$\sf x^2+6x-6=x^2-5$

$\sf x^2-x^2+6x-6=-5$

$\sf 6x-6=-5$

$\sf 6x=-5+6$

$\sf 6x=1$

$\sf x=\dfrac{1}{6}$