Chapter 16.8, Problem 2WE

To determine

To calculate: The value of the determinant,

  $\left|\begin{array}{ccc}-2& 0& 12\\ 4& 0& 0\\ 3& 0& 6\end{array}\right|$

Answer to Problem 2WE

The value of the determinant is $0$ .

Explanation of Solution

Given information:

The determinant:

  $\left|\begin{array}{ccc}-2& 0& 12\\ 4& 0& 0\\ 3& 0& 6\end{array}\right|$

Formula used:

If either an entire row or an entire column is 0 then the value of determinant is 0.

Calculation:

Consider the determinant

  $\left|\begin{array}{ccc}-2& 0& 12\\ 4& 0& 0\\ 3& 0& 6\end{array}\right|$

Observe that all entries of second column are zero.

Recall that if either an entire row or an entire column is 0 then the value of determinant is 0.

Therefore,

  $\left|\begin{array}{ccc}-2& 0& 12\\ 4& 0& 0\\ 3& 0& 6\end{array}\right|=0$

Thus, the value of the determinant is $0$ .