Week 2 Discussion A First Course in Linear Algebra - Exercises C10 -(Page 278)

C23 Doing the computations by hand, find the determinant of the matrix below.

\[\begin{pmatrix} 1 & 3 & 2\\ 4 & 1 & 3 \\ 1 & 0 & 1 \\ \end{pmatrix} \]

Solution

\[\begin{pmatrix} 1 & 3\\ 0 & 1 \\ \end{pmatrix} + 3* \begin{pmatrix} 4 & 3\\ 1 & 1 \\ \end{pmatrix} + 2*\begin{pmatrix} 4 & 1\\ 1 & 0 \\ \end{pmatrix}\]

==> (1-0)+3(4-3)+2(0-1)

= 1 + 3 - 2 = 2