$$A=\begin{pmatrix}
1 & -1 & 0 & 2 \\
2 & 1 & 0 & 0 \\
1 & 1 & 2 & 2 \\
0 & 0 & 1 & 1 \\
\end{pmatrix}$$
With the lower determinant method, I got $det(A)=-2$ but my task is to use Gauss method to find out determinant. I know that for a triangular matrix $B$, $det(B)=\prod b_{ii}$ i.e. the trace (product of diagonal things). Now I can make this into a triangular matrix by Gauss Jordan but I cannot understand yet what does it mean that solve the determinant with Gauss method or Gauss rule whatever you call it? I am on page 741 XI.5:4, here (not English), it should be trivial problem but stuck to this.
ERR: what is the problem with this, trying to use the G.E.?
Best Answer
Performing Gaussian Elimination on $$ A=\begin{pmatrix} 1 & -1 & 0 & 2 \\ 2 & 1 & 0 & 0 \\ 1 & 1 & 2 & 2 \\ 0 & 0 & 1 & 1 \\ \end{pmatrix}$$ we get $$ \begin{pmatrix} 1 & -1 & 0 & 2 \\ 0 & ? & ? & ? \\ 0 & 0 & ? & ? \\ 0 & 0 & 0 & ? \\ \end{pmatrix}$$ which has the determinant (see property 9 here): $$ 1 \times ?\times ? \times ? = -2 $$ Since this is a
(homework)question, I will let you fill in all the blanks.