Concept:The determinant of a matrix with linearly dependent rows is zero.Explanation:For matrix A=147258369:Observe that R3−R2=(3,3,3) and R2−R1=(3,3,3), so R3=2R2−R1.Thus the rows are linearly dependent, so det(A)=0.Alternatively, compute directly:det(A)=1(5⋅9−6⋅8)−2(4⋅9−6⋅7)+3(4⋅8−5⋅7)=1(45−48)−2(36−42)+3(32−35)=−3−2(−6)+3(−3)=−3+12−9=0.Answer:0