Question

What are the values of x and y in the matrix equation below? (PICTURED)
Answer options:
1.) x=3
y=+8, -8
2.)x=3
y=+4,-4
3.)x=-3
y=+4,-4
4.) x=-3
y=4

Answer 1

Given the matrix equation:

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

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

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

Now, comparing left hand side with right side, we have:

$4-8x = 28$                      and                 $y^{2}-16=0$

i.e., $-8x = 28-4$              and                 $y^{2}=16$

i.e., $-8x=24$                    and                $y=\pm\sqrt{16}$

i.e., $x=\frac{24}{-8}$        and                 $y=\pm4$

i.e., $x = -3$                      and                 $y=+4,-4$

Hence, third option is correct.

Answer 2

Answer:

4.) x=-3 and y=4

Step-by-step explanation:

[x+4] + [-9x] = [28]

First plug in x into the equation

[-3+4] + [-9(-3)] = [28]

[1] + [27] = [28]

1+27=28 (True)

Next, plug in y into the equation

[y^2+1] + [-17] = [0]

[(4)(4)+1] + [-17] = [0]

[16+1] + [-17] = [0]

[17] + [-17] =[0]

17 + -17=0 (True)

The Answer is D- X = -3 and Y= 4