Chapter MA, Problem 1.1MA

To determine

The value of the determinant V.

Explanation of Solution

Given:

  $V=\left|\begin{array}{ccc}2& 5& 4\\ 4& 1& 6\\ 3& 0& 1\end{array}\right|$

Calculation:

Write the expression for the determinant.

  $\begin{array}{c}V=\left|\begin{array}{ccc}2& 5& 4\\ 4& 1& 6\\ 3& 0& 1\end{array}\right|\\ V=2\cdot \left|\begin{array}{cc}1& 6\\ 0& 1\end{array}\right|-5\cdot \left|\begin{array}{cc}1& 6\\ 0& 1\end{array}\right|+4\cdot \left|\begin{array}{cc}1& 6\\ 0& 1\end{array}\right|\\ =2\left(1-0\right)-5\left(4-18\right)+4\left(0-3\right)\\ =2+70-12\\ =60\end{array}$

Thus, the determinant for the given V is 60 units.