C23 (p.353)

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

Solution 1

\[ \begin{bmatrix} 1 & 3 & 2 \\ 4 & 1 & 3 \\ 1 & 0 & 1 \end{bmatrix} = 1 * \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix} + (-3) * \begin{bmatrix} 4 & 3 \\ 1 & 1 \end{bmatrix} + 2 * \begin{bmatrix} 4 & 1 \\ 1 & 0 \end{bmatrix} = -4 \]

Solution 2 (upper triangular form)

\[ \begin{bmatrix} 1 & 3 & 2 \\ 4 & 1 & 3 \\ 1 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 3 & 2 \\ 0 & -11 & -5 \\ 1 & 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 & 3 & 2 \\ 0 & -11 & -5 \\ 0 & 0 & 0.363636363636364 \end{bmatrix} \]

1*(-11)*4/11
## [1] -4

Using det()

det(A)
## [1] -4