Question

Calcule o valor de x, y e z de modo que cada igualdade seja verdadeira. Alguém sabe fazer ou explicar??? Preciso urgentemente.

Answer 1

Explicação passo-a-passo:

a) $\left[\begin{array}{cc} 3&x \\ 4&z^2 \end{array}\right]+\left[\begin{array}{cc} -1&2x \\ y&-1 \end{array}\right]=\left[\begin{array}{cc} 2&6 \\ -1&0 \end{array}\right]$

$\left[\begin{array}{cc} 3-1&x+2x \\ 4+y&z^2-1 \end{array}\right]=\left[\begin{array}{cc} 2&6 \\ -1&0 \end{array}\right]$

Igualando os elementos correspondentes:

$\bullet~~x+2x=6$

$3x=6$

$x=\dfrac{6}{3}$

$x=2$

$\bullet~~4+y=-1$

$y=-1-4$

$y=-5$

$\bullet~~z^2-1=0$

$z^2=1$

$z=\pm\sqrt{1}$

$z=1$ ou $z=-1$

b) $\left[\begin{array}{ccc} x&-y&\frac{z}{2} \end{array}\right]-\left[\begin{array}{ccc} 2&3y&z \end{array}\right]=\left[\begin{array}{ccc} 5&2&-\frac{5}{2} \end{array}\right]$

$\left[\begin{array}{ccc} x-2&-y-3y&\frac{z}{2}-z \end{array}\right]=\left[\begin{array}{ccc} 5&2&-\frac{5}{2} \end{array}\right]$

Igualando os elementos correspondentes:

$\bullet~~x-2=5$

$x=5+2$

$x=7$

$\bullet~~-y-3y=2$

$-4y=2$

$y=\dfrac{2}{-4}$

$y=\dfrac{-1}{2}$

$\bullet~~\dfrac{z}{2}-z=\dfrac{-5}{2}$

$\dfrac{z-2z}{2}=\dfrac{-5}{2}$

$\dfrac{-z}{2}=\dfrac{-5}{2}$

$z=5$

c) $\left[\begin{array}{c} -2 \\ 4 \\ y \\ z \end{array}\right]+\left[\begin{array}{c} 4x \\ 6 \\ y^2 \\ 0 \end{array}\right]-\left[\begin{array}{c} 0 \\ 9 \\ 6 \\ 1 \end{array}\right]=\left[\begin{array}{c} x \\ 1 \\ -6 \\ \frac{z}{3} \end{array}\right]$

$\left[\begin{array}{c} -2+4x-0 \\ 4+6-9 \\ y+y^2-6 \\ z+0-1 \end{array}\right]=\left[\begin{array}{c} x \\ 1 \\ -6 \\ \frac{z}{3} \end{array}\right]$

Igualando os elementos correspondentes:

$\bullet~~-2+4x-0=x$

$4x-x=2$

$3x=2$

$x=\dfrac{2}{3}$

$\bullet~~y+y^2-6=-6$

$y+y^2=0$

$y\cdot(1+y)=0$

$y'=0$

$1+y=0~\longrightarrow~y"=-1$

$y=0$ ou $y=-1$

$\bullet~~z+0-1=\dfrac{z}{3}$

$z-1=\dfrac{z}{3}$

$3\cdot(z-1)=z$

$3z-3=z$

$3z-z=3$

$2z=3$

$z=\dfrac{3}{2}$