Question

(UFGRS) Determine o valor de x, y e z, para que: ... Resto da pergunta na imagem, pois é uma matriz.

Answer 1

Oi Vitória.

Basta igualar e resolver.

Primeiro temos um sistema.

$3x+y=7\\ 5x-y=1\\ 8x=8\\ x=\frac { 8 }{ 8 } \\ \\ x=1\\ \\ \\ 3x+y=7\\ 3(1)+y=7\\ 3+y=7\\ y=7-3\\ y=4$

Agora igualando para achar o z.

$z+6=4\\ z=4-6\\ z=-2$

Answer 2

$a_{11}=3x+y=7 \\\\ a_{22}=5x-y=1 \\ \\a_{23}=z+6=4 \\ \\ \\ a_{11}+a_{22}: \\ \\ (3x+5x)+(y+(-y))=7+1 \\ \\ 8x+y-y=8 \\ \\ 8x=8 \\ \\ x=8/8 \\ \\ x=1$



$a_{22}: \\ \\ 5x-y=1 \\ \\ 5(1)-y=1 \\ \\ 5-y=1 \\ \\ 5-1=y \\ \\ 4=y \\ \\ \\ a_{23}: \\ \\ z+6=4 \\ \\ z=4-6 \\ \\ z=-2$



$\left[\begin{array}{ccc}3x+y&2&3\\4&5x-y&z+6\\\end{array}\right]= \left[\begin{array}{ccc}7&2&3\\4&1&4\\\end{array}\right] \\ \\ \\ \left[\begin{array}{ccc}3(1)+(4)&2&3\\4&5(1)-(4)&(-2)+6\\\end{array}\right]=\left[\begin{array}{ccc}7&2&3\\4&1&4\\\end{array}\right] \\ \\ \\ \left[\begin{array}{ccc}7&2&3\\4&1&4\\\end{array}\right]=\left[\begin{array}{ccc}7&2&3\\4&1&4\\\end{array}\right]$