Exercise 5

Express each of these in terms of $\mathchoice{\left|H\right|}{|H|}{|H|}{|H|}$.

• $\begin{vmatrix}h_{3,1}&h_{3,2}&h_{3,3}\\ h_{2,1}&h_{2,2}&h_{2,3}\\ h_{1,1}&h_{1,2}&h_{1,3}\end{vmatrix}$

• $\begin{vmatrix}-h_{1,1}&-h_{1,2}&-h_{1,3}\\ -2h_{2,1}&-2h_{2,2}&-2h_{2,3}\\ -3h_{3,1}&-3h_{3,2}&-3h_{3,3}\end{vmatrix}$

• $\begin{vmatrix}h_{1,1}+h_{3,1}&h_{1,2}+h_{3,2}&h_{1,3}+h_{3,3}\\ h_{2,1}&h_{2,2}&h_{2,3}\\ 5h_{3,1}&5h_{3,2}&5h_{3,3}\end{vmatrix}$