Question

What are the values of x and y in the matrix equation below?

Answer 1

Answer : value of x and y in the matrix equation is:

x = -3

y = +4, -4

Step-by-step explanation :

The matrix expression is:

$\left[\begin{array}{ccc}x+4\\y^2+1\end{array}\right]+\left[\begin{array}{ccc}-9x\\-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]$

First we have to add left hand side matrix.

$\left[\begin{array}{ccc}(x+4)+(-9x)\\(y^2+1)+(-17)\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]$

Now we have to add left hand side terms.

$\left[\begin{array}{ccc}x+4-9x\\y^2+1-17\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]$

$\left[\begin{array}{ccc}4-8x\\y^2-16\end{array}\right]=\left[\begin{array}{ccc}28\\0\end{array}\right]$

Now we have to equating left hand side matrix to right hand matrix, we get:

$\Rightarrow 4-8x=28\text{ and }y^2-16=0\\\\\Rightarrow 8x=4-28\text{ and }y^2=16\\\\\Rightarrow x=-3\text{ and }y=\pm 4$

Therefore, the value of x and y in the matrix equation is -3 and +4, -4 respectively.