Chapter 3 Linear Systems and Matrices - 3.7 Evaluate Determinants and Apply Cramer's Rule - 3.7 Exercises - Skill Practice - Page 207: 14

$129$

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 $D=-7(2\cdot6-(-4)\cdot1)-4(1\cdot6-(-4)\cdot-10)+5(1\cdot1-2\cdot-10)=-7(16)-4(-34)+5(21)=129.$