Question

qual a resposta correta

Answer 1

Resposta:

b) 8/3

Explicação passo-a-passo:

Sabemos que A = $\left[\begin{array}{ccc}2&5&1\\-1&4&-3\\3&0&2\end{array}\right]$, então:

$A^t = \left[\begin{array}{ccc}2&-1&3\\5&4&0\\1&-3&2\end{array}\right]$

Agora vamos descobrir quem é -1/3.A:

$-1/3.\left[\begin{array}{ccc}2&5&1\\-1&4&-3\\3&0&2\end{array}\right] \\\\\left[\begin{array}{ccc}-2/3&-5/3&-1/3\\1/3&-4/3&1\\-1&0&-2/3\end{array}\right]$

$A^t+(-1/3.A)\\\\\left[\begin{array}{ccc}4/3&-8/3&8/3\\16/3&8/3&1\\0&-3&4/3\end{array}\right]$

Como $A^t + (-1/3.A) = \left[\begin{array}{ccc}2x+y&5x+y&8/3\\16/3&8/3&1\\0&-3&4/3\end{array}\right]$, então:

{ 2x +y = 4/3

{ 5x +y = -8/3 .( -1)

{ 2x +y = 4/3

{      -3x = 4

-3x =4

x = -4/3

2.(-4/3) +y = 4/3

-8/3 +y = 4/3

y = 4/3 +8/3

y = 12/3

y = 4

x + y

-4/3 + 4

8/3

Dúvidas só perguntar!