Exercise 6

Each pair of matrices differ by one row operation. Use this operation to compare $\det(A)$ with $\det(B)$.

• $A=\begin{pmatrix}1&2\\ 2&3\end{pmatrix}$, $B=\begin{pmatrix}1&2\\ 0&-1\end{pmatrix}$

• $A=\begin{pmatrix}3&1&0\\ 0&0&1\\ 0&1&2\end{pmatrix}$, $B=\begin{pmatrix}3&1&0\\ 0&1&2\\ 0&0&1\end{pmatrix}$

• $A=\begin{pmatrix}1&-1&3\\ 2&2&-6\\ 1&0&4\end{pmatrix}$, $B=\begin{pmatrix}1&-1&3\\ 1&1&-3\\ 1&0&4\end{pmatrix}$