Let A 1 0 1 beta 2 1 0 1 q Determine all values of q for wh

Let A = [1 0 1 -beta 2 1 0 1 q]. Determine all values of q for which A is singular.

Solution

Find the determinant of the matrix:

A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0.

If A is singular then detA =0

So, 1[ 2q - 1 ] +1[ 0 - 0 ] =0

2q - 1 =0

q = 1/2