Q54. - Algebra 2

Question

Use a graphing calculator to find the value of the following determinant.

 

$\left|\begin{array}{ccc}10& 20& 30\\ 40& 50& 60\\ 70& 80& 90\\ & & \end{array}\right|$

Step-by-Step Solution

Answer

The value of the determinant is 0.

Step 1- Apply the concept of determinant.

The determinant is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the linear map represented by the matrix.

Step 2- Step description.

Consider the determinant $\left|\begin{array}{ccc}10& 20& 30\\ 40& 50& 60\\ 70& 80& 90\\ & & \end{array}\right|$.

 

Use a graphing calculator and find the value of the determinant as follows:

 

 $\begin{array}{l}=10(4500-4800)-20(3600-4200)+30(3200-3500)\\ =0\end{array}$

Step 3- Step description.

Therefore, the value of the determinant is 0.