Chapter 2.2, Problem 24E

Verify the formulas in parts (a) and (b) and then make a conjecture about a general result of which these results are special cases.

$\det \left[\begin{array}{ccc}0& 0& a_{13}\\ 0& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]=-a_{13}{a}_{22}{a}_{31}$

$\det \left[\begin{array}{cccc}0& 0& 0& a_{14}\\ 0& 0& a_{23}& a_{24}\\ 0& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]=a_{14}{a}_{23}{a}_{32}{a}_{41}$