Question

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

Answer 1

Answer: choice C

Explanation:

Answer 2

`x=2`

Explanation:

The given matrix equation is ;

`(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}(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}(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;

`(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.

`(3)/(2)x-2=1`

`(3)/(2)x=1+2`

`(3)/(2)x=3`

`(1)/(2)x=1`

`x=2`