Given a matrix $$A =\begin{pmatrix}1& 1& 1\\−2& 1& 3\\3& 2& 1\end{pmatrix}$$
use Gaussian elimination to compute the determinant $\det(A)$ of $A$ and to solve the system of linear equations $AX = b$, where $X = (X_1,X_2,X_3)^T$ is the vector of unknowns and $b = (1, 0, 1)^T$ . The solution should be represented by simple fractions. Show your working.
I immediately assume to convert the matrix to the form:
$$x + y + z = \\ -2x + y + z = \\ 3x + 2y + z =$$
My question is what are each of these equal to? I assumed it was 1 , 0, 1 respectively as left to right is top to bottom, but I am not so sure. Thank you for any help.