What $3 \times 3$ matrix has the effect of these steps, in this order?
Subtract row $1$ from row $2$,
Add row $1$ to row $2$,
Add row $2$ from row $3$,
Subtract half of row $3$ from row $1$,
I have no idea how to solve a question in this form, any help is appreciated.
On
Let your $3\times 3$ matrix be $$ A=\begin{pmatrix} x & y & z \\ a & b & c \\ k & m & n \\ \end{pmatrix}\\ $$ So now, we need to do some row operations:$$ \begin{pmatrix} x & y & z \\ a & b & c \\ k & m & n \\ \end{pmatrix} \xrightarrow{r_2\rightarrow r_2-r_1}\begin{pmatrix} x & y & z \\ a-x & b-y & c-z \\ k & m & n \\ \end{pmatrix} \xrightarrow{r_2\rightarrow r_1+r_2} \begin{pmatrix} x & y & z \\ a & b & c \\ k & m & n \\ \end{pmatrix}\xrightarrow{r_3\rightarrow r_2+r_3}\begin{pmatrix} x & y & z \\ a & b & c \\ a+ k & b+m &c+ n \\ \end{pmatrix}\xrightarrow{r_1\rightarrow r_1-\frac{r_3} 2}\begin{pmatrix} x-\frac{a+k}2 & y-\frac{b+m}2 & z-\frac{c+n}2 \\ a & b & c \\ a+ k & b+m &c+ n \\ \end{pmatrix} $$
HINT: A matrix that accomplishes the first operation is $$\pmatrix{ 1 &0 &0\\ -1 &1 &0\\ 0&0&1 } $$ If you don't see why, multiply a general $3\times 3$ matrix on the left by this matrix. Now you should be able to come up with the matrices for the other operations.
Do you see how to combine them? What would be the result of performing all those operations on a matrix? How can you express it with a single matrix?