Question

3 1 0 1
1 3 1 0
0 1 3 1
0 0 1 3

find the determinant of this matrix. I do not remember how to do it step by step

Answer 1

There might be a trick to this one.

But there are a lot of zeros in the matrix, so you can exploit that. One way is to just use cofactor expansion.
So the determinant is just
\[3\left( (3 & 1 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right) + (-1)1\left( (1 & 0 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right)].

If you’ve forgotten cofactor by expansion, it’s hard to explain typing it here, but I’d recommend either going to Paul’s Online Math Notes for written explanation with examples or khanacademy.org for spoken explanation of it.

Answer 2

\[3\left( (3 & 1 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right) + (-1)1\left( (1 & 0 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right)]\

Answer 3

I apologize, let me try that one last time.
\[3\left( (3 & 1 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right) + (-1)1\left( (1 & 0 & 0 \ 1 & 3 & 1 \ 0 & 1 & 3) \right)\]