# Chapter 12 Sequences and Series - Cumulative Review - Page 848: 15

$360.$

#### Work Step by Step

For a 3x3 matrix: $\left[\begin{array}{rrr} a & b & c \\ d &e & f \\ g &h & i \\ \end{array} \right]$ The determinant is given by: $D=a(ei-fh)-b(di-fg)+c(dh-eg).$ Hence here $D=0(13\cdot(-1)-(-4)\cdot4)-5(10\cdot(-1)-(-4)\cdot(-5))+2(10\cdot4-13\cdot(-5))=0(3)-5(-30)+2(105)=360.$

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