Question

Q7 If the matrix
is singular, find the value of x.​

Answer 1

x=0,3

A=

3−x2−224−x−421−1−x

If the matrix is singular, its determinant has to be zero.

⇒(3−x)[(4−x)(−1−x)+4]−2[2(−1−x)+2]+2[−8+2(4−x)]=0

⇒(3−x)[−4−4x+x+x2+4]−2[−2−2x+2]+2[−8+8−2x]=0

⇒(3−x)[x2−3x]+4x−4x=0

⇒(3−x)x(x−3)=0

⇒x=0,3