(I don't know how to make a matrix here, someone please correct it into a better format, thanks~)
So I'm applying the Gaussian Elimination to find the determinant for this matrix:
$\begin{pmatrix} 0&1&3\\ 1&2&0\\ 0&3&4\\ \end{pmatrix}$
So, I switched row $1$ and $2$: $\begin{pmatrix} 1&2&0\\ 0&1&3\\ 0&3&4\\ \end{pmatrix}$
Then, add the multiple of $-3$ of row $2$ to the third row: $\begin{pmatrix} 1&2&0\\ 0&1&3\\ 0&0&-5\\ \end{pmatrix}$
So the determinant I got is $-5$, however the answer key said it's $5$. Some1 point out what I have done wrong? Thank you!!
$\endgroup$ 21 Answer
$\begingroup$When you apply Gaussian Elimination to find the determinant, you have to multiply by $(-1)$ at the end for every row switches you have applied.
$\endgroup$ 1
