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√(16)`

i.e.,
`x=(24)/(-8)` and
`y=\pm4`

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

Hence, third option is correct.