Question

Dadas as matrizes A= x+y 1
-5 x-y
e B= 3 1
-5 -1
Calcule x e y de modo que A = B

Answer 1

Olá!

Temos as seguintes matrizes:

$A = \left[\begin{array}{cc}x+y&1\\-5&x-y\\\end{array}\right]$

$B = \left[\begin{array}{cc}3&1\\-5&-1\\\end{array}\right]$

Sendo:

$A=B$

$\left[\begin{array}{cc}x+y&1\\-5&x-y\\\end{array}\right] = \left[\begin{array}{cc}3&1\\-5&-1\\\end{array}\right]$

Temos:

$\left \{ {{x\:+\:\diagup\!\!\!\!\!y\:=\:3} \atop {x\:-\:\diagup\!\!\!\!\!y\:=\:-1}} \right.$

$2x = 2$

$x = \dfrac{2}{2}$

$\boxed{\boxed{x = 1}}\end{array}}\qquad\checkmark$

Sabendo que:

$x+y = 3$

$1 + y = 3$

$y = 3-1$

$\boxed{\boxed{y = 2}}\end{array}}\qquad\checkmark$

Espero ter ajudado! =)