Chapter 16.7, Problem 8WE

To determine

To Find:Expansion of the determinant about column one:

  $\left|\begin{array}{ccc}0& -2& 4\\ 1& 3& -1\\ 0& 0& 5\end{array}\right|$

Answer to Problem 8WE

10

Explanation of Solution

Given:

  $\left|\begin{array}{ccc}0& -2& 4\\ 1& 3& -1\\ 0& 0& 5\end{array}\right|$

Formula Used:

1. Determinant of a 3 x 3 matrix:

  $\left|\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right|=a.\left|\begin{array}{cc}e& f\\ h& i\end{array}\right|-d.\left|\begin{array}{cc}b& c\\ h& i\end{array}\right|+g.\left|\begin{array}{cc}b& c\\ e& f\end{array}\right|$

2. Determinant of a 2 x 2 matrix:

  $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-cb$

  $\begin{array}{l}\left|\begin{array}{ccc}0& -2& 4\\ 1& 3& -1\\ 0& 0& 5\end{array}\right|=0\left|\begin{array}{cc}3& -1\\ 0& 5\end{array}\right|-1\left|\begin{array}{cc}-2& 4\\ 0& 5\end{array}\right|+0\left|\begin{array}{cc}-2& 4\\ 3& -1\end{array}\right|\\ \Rightarrow 0-1(-2(5))-0\\ \Rightarrow 10\end{array}$