Question

Pergunta sobre matriz,

Answer 1

O usuário pediu para que eu resolvesse só a 6, avisando pra não denunciarem.
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$\left[\begin{array}{cc}5x-2y&5\\3x+y&2\end{array}\right]-\left[\begin{array}{cc}x+2&-3\\2y-1&2\end{array}\right]=\left[\begin{array}{cc}3&8\\-2&0\end{array}\right] \\\\\\ \left[\begin{array}{cc}5x-2y-(x+2)&5-(-3)\\3x+y-(2y-1)&2-2\end{array}\right]=\left[\begin{array}{cc}3&8\\-2&0\end{array}\right]\\\\\\ \left[\begin{array}{cc}5x-2y-x-2&5+3\\3x+y-2y+1&0\end{array}\right]=\left[\begin{array}{cc}3&8\\-2&0\end{array}\right]$

$\left[\begin{array}{cc}4x-2y-2&8\\3x-y+1&0\end{array}\right]=\left[\begin{array}{cc}3&8\\-2&0\end{array}\right]$

As matrizes serão iguais se seus elementos correspondentes forem iguais:

$4x-2y-2=3\\4x-2y=3+2\\4x-2y=5$

$3x-y+1=-2\\3x-y=-2-1\\3x-y=-3$

$5=5 \\\\0=0$

Sistema:

$\left \{ {{4x-2y=5} \atop {3x-y=-3}} \right.$

Multiplicando a segunda equação por -2:

$\left \{ {{4x-2y=5} \atop {-6x+2y=6}}\right.$

Somando as equações:

$4x-6x-2y+2y=5+6\\-2x=11\\x=-11/2$

$4x-2y=5\\4(-11/2)-2y=5\\2(-11)-2y=5\\-22-2y=5\\-22-5=2y\\2y=-27\\y=-27/2$