Question

Solve using matrices
x-2y+z=10
3x+y=5
7x+2z=2

Answer 1

This method is also called "Gauss jordan reduction", it consists on representing a system of equalities and tweaking the matrix until you get a matrix that looks like:
\[\left[\begin{matrix}a & 0 & 0 & K \\ 0 & b & 0 & K'\\ 0 & 0 & c & K'' \end{matrix}\right]\]
The reasong is quite simple, because that matrix implies that:
\[ax=K\]
\[by=K'\]
\[cz=K''\]

So, applying it to the system of equation you posted, the matrix will look like this:
\[\left[\begin{matrix}1 & -2 & 1 & 10 \\ 3 & 1 & 0 & 5\\ 7& 0 & 2 & 2\end{matrix}\right]\]
So, all you have to do is apply the matrix properties until you get a matrix with the same structur as the first I mentioned.

Answer 2

Would you mind going step by step with me? I am confused