Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - Guided Practice for Examples 1 and 2 - Page 204: 2

$-21$

We know that for a matrix \[ \left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right] \] the determinant is: $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=4(-2\cdot1-(-1)\cdot5)-(-1)(-3\cdot1-(-1)\cdot0)+2(-3\cdot5-(-2)\cdot0)=4(3)+1(-3)+2(-15)=-21$