Question

Determine o valor De A da matriz ​

Answer 1

Explicação passo-a-passo:

Pelo Teorema de Binet:

$\sf det~(M\cdot N)=det~(M)\cdot det~(N)$

$\sf det~(M)=3\cdot0\cdot(-3)+3\cdot6\cdot1+2\cdot2\cdot0-1\cdot0\cdot2-0\cdot6\cdot3-(-3)\cdot2\cdot3$

$\sf det~(M)=-0+18+0-0-0+18$

$\sf det~(M)=36$

$\sf det~(N)=0\cdot2\cdot0+0\cdot0\cdot a+1\cdot0\cdot1-a\cdot2\cdot1-1\cdot0\cdot0-0\cdot0\cdot0$

$\sf det~(N)=0+0+0-2a-0-0$

$\sf det~(N)=-2a$

Assim:

$\sf 36\cdot(-2a)=-360$

$\sf -72a=-360$

$\sf a=\dfrac{-360}{-72}$

$\sf a=5$