Question

Find the value of x for which the matrix `A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)]` is singular.

Answer 1

Correct Answer - `pm 1`
`A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)]`
We have
`|A|=(2/x) |(x,2x^(2)),(1//x,2)|+|(1,2x^(2)),(1,2)|+2|(1,x),(1,1//x)|`
`=2/x (0)+2-2x^(2)+2 (1/x-x)`
`=(2x(1-x^(2))+2(1-x^(2)))/(x)`
`=(2(x+1)^(2)(1-x))/(x)`
Now, `|A|=0" "implies" "x= pm 1`