Worksheet 22

1. Compute the determinant of \(\begin{pmatrix} 1 & -1 & 0 \\ 2 & 1 & 1 & \\ -1 & 1 & 3 \end{pmatrix}\) by hand using Gaussian Elimination.

2. Given an $m \times n$ matrix $A$ and an $n \times m$ matrix $B$, if $m < n$, what can you say about \(\det (B A)?\)

3. What can you say about the determinant of an orthogonal matrix?