Chapter 16.8, Problem 2OE

To determine

To calculate: The value of the determinant,

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

Answer to Problem 2OE

The value of the determinant is $3$ .

Explanation of Solution

Given information:

The value of the determinant:

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

Formula used:

The value of determinant gets k times when all entries either in a row or in a column gets multiplied by number say k .

Calculation:

Consider the determinant

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

It is provided that the value of the determinant

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

Observe that the third column is multiplied by 3.

The value of determinant gets k times when all entries either in a row or in a column gets multiplied by number say k .

  $\begin{array}{c}\left|\begin{array}{ccc}0& 3& 3\\ 1& 2& 0\\ -1& 2& 3\end{array}\right|=3\left(1\right)\\ =3\end{array}$

Thus, the value of the determinant is $3$ .