Chapter 6.3, Problem 65E

To determine

To find: the value of given determinant.

Answer to Problem 65E

  $-12$

Explanation of Solution

Given information:

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

Calculation:

The value of determinant can be evaluated as follows:

  $\begin{array}{c}\left|\begin{array}{ccc}\begin{array}{l}-2\\ 1\\ -3\end{array}& \begin{array}{l}4\\ -1\\ 4\end{array}& \begin{array}{l}-1\\ \text{ 0}\\ \text{ 5}\end{array}\end{array}\right|=-2\left|\begin{array}{cc}\begin{array}{l}-1\\ 4\end{array}& \begin{array}{l}0\\ 5\end{array}\end{array}\right|-4\left|\begin{array}{cc}\begin{array}{l}1\\ -3\end{array}& \begin{array}{l}0\\ 5\end{array}\end{array}\right|-1\left|\begin{array}{cc}\begin{array}{l}1\\ -3\end{array}& \begin{array}{l}-1\\ 4\end{array}\end{array}\right|\\ =-2\left(-5\times 0\right)-4\left(5\times 0\right)-1\left(4\times 3\right)\\ =-2\left(0\right)-4\left(0\right)-1\left(12\right)\\ =0-0-12\\ =-12\end{array}$

Thus the value is $-12$ .