Question

HELP ASAP!! please show work!!! what is the value of x in the matrix equation below?

Answer 1

Answer:

$x=2$

Step-by-step explanation:

The given matrix equation is ;

$\frac{3}{2}\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y \left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

We multiply the scalars to get;

$\left[\begin{array}{cc}\frac{3}{2}x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

We simplify to get;

$\left[\begin{array}{cc}\frac{3}{2}x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]$

By the equality property of matrices, we can write the following equations;

$\frac{3}{2}x+y=z...(1)$

$6+2y=2$

$2y=2-6$

$2y=-4$

$y=-2$

Also;

$12+3y=6z$

$\Rightarrow 12+3(-2)=6z$

$\Rightarrow 12-6=6z$

$\Rightarrow 6=6z$

$\Rightarrow z=1$

We substitute these values into equation (1) to find x.

$\frac{3}{2}x-2=1$

$\frac{3}{2}x=1+2$

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

$\frac{1}{2}x=1$

$x=2$