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