Question

Which matrix equation represents the system of equations?

{-x+ 2y = 0
y= -2

Answer 1

We are given a system of equations,

`\begin{cases}-x+2y=0\\y=-2\\ \end{cases}`

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

`\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}`

The matrix will then be applied to the vector (lower dimensions on top),

`\begin{bmatrix}x\\y\\ \end{bmatrix}`

And the result vector will be whats on the other side of equals sign,

`\begin{bmatrix}0\\-2\\ \end{bmatrix}`

So to put everything together,

`\begin{bmatrix}-1&2\\0&1\\ \end{bmatrix}\begin{bmatrix}x\\y\\ \end{bmatrix}=\begin{bmatrix}0\\-2\\ \end{bmatrix}`

Hope this helps :)