Find the values of x for which matrix `[(3,-1+x,2),(3,-1,x+2),(x+3,-1,2)]` is singular.

Explanation

Given matrix is singular
`:. |(3,x-1,2),(3,-1,x+2),(x+3,-1,2)|=0`
`implies |(0,x,-x),(3,-1,x+2),(x+3,-1,2)|=0" "[R_(1) rarr R_(1)-R_(2)]`
`implies |(0,x,-x),(-x,0,x),(x+3,-1,2)|=0" "[R_(2) rarr R_(2)-R_(3)]`
`implies |(0,x,0),(-x,0,x),(x+3,-1,1)|=0" "[C_(3) rarr C_(3)+C_(2)]`
`implies -x[(-x)-x(x+3)]=0`
`implies x(x^(2)+4x)=0`
`implies x=0, -4`