For what value if x matrix A= [ x-1 1 1 1 x-1 1 1 1 x-1]is singular matrixx - Maths - Determinants

Question

For what value if x matrix A= [ x-1 1 1 1 x-1 1 1 1 x-1]is
singular matrixx?

Priyanka Kedia · Accepted Answer

Given, matrix A=x-1111x-1111x-1 is singular
We know that, A matrix is singular iff its determinant is zero
 So,detA=0⇒x-1x-1x-1-1-11x-1-1+11×1-1x-1=0⇒x-13-x-1-x-2+2-x=0⇒x3-1-3xx-1-x+1-x+2+2-x=0⇒x3-1-3x2+3x-3x+5=0⇒x3-3x2+4=0⇒x+1x-22=0⇒x=-1, and 2

For what value if x matrix A= [ x-1 1 1 1 x-1 1 1 1 x-1]is singular matrixx?