Q53. - Algebra 2

Question

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

 

$\left|\begin{array}{ccc}8& 6& -5\\ 10& -7& 3\\ 9& 14& -6\\ & & \end{array}\right|$

Step-by-Step Solution

Answer

The value of the determinant is$-493$.

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 $\left|\begin{array}{ccc}8& 6& -5\\ 10& -7& 3\\ 9& 14& -6\\ & & \end{array}\right|$.

 

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

 

 $\begin{array}{l}=8(42-42)-6(-60-27)-5(140+63)\\ =-6(-87)-5\left(203\right)\\ =-493\end{array}$

Step 3- Step description.

Therefore, the value of the determinant is$-493$.