Question

(Fatec-2003) Seja a matriz A=( matrix 1&b\\ a&1 matrix ) tal que A ^ 2 =( matrix -19&-8\\ 10&-19 matrix )i verdade que 8) bé igual a: a + b​

Answer 1

Resposta:

a=5

b=-4

Explicação passo-a-passo:

$A=\left[\begin{array}{cc}1&b\\a&1\end{array}\right] \\\\A^2=\left[\begin{array}{cc}-19&-8\\10&-19\end{array}\right]$

$A*A=\left[\begin{array}{cc}1*1+b*a&1*b+b*1\\1*a+a*1&a*b+1*1\end{array}\right]$

1+ba = -19

2a=10

2b=-8

ab+1 =-19

a=5

b=-4

-20+1=-19