Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 13

$-34.$

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=5(9\cdot0-(-2)\cdot(-4))-0(-3\cdot0-(-2)\cdot1)+2(-3\cdot-4-9\cdot1)=5(-8)-0(2)+2(3)=-34.$