Expert: Steve Holleran - 2/24/2008

Question
what does it mean when a question ask
Determine all values of x so that the matrix A has an inverse
and matrix A is [3 2 4]
                x 1 -2
                -3 5 x

Answer
Hi Melissa,

A matrix will have an inverse as long as its determinant is not =0.

So, find the determinant and set it = 0, then the matrix will have an inverse for all values of x except these.

For the determinant, I got:

 |A| = (3x + 12 + 20x) - (-12 -30 + 2x^2) = 0

         -2x^2 + 23x + 54 = 0

          2x^2 - 23x -54 = 0

This factors :   (x + 2)(2x - 27)= 0 so x = -2, 27/2

So this matrix is invertible for x not = -2, 27/2

Hope this helps
Steve