Exercise C25 (Page 278)

Doing the computations by hand, find the determinant of the matrix below: \[ \begin{bmatrix} 3 & -1 & 4\\ 2 & 5 & 1\\ 2 & 0 & 6\\ \end{bmatrix} \]

Define Matrix

A = matrix(c(3, 2, 2, -1, 5, 0, 4, 1, 6), ncol = 3, nrow = 3)

Solve with R

det(A)
## [1] 60

Solve by Hand

# 3 * det|5,1,0,6|

determinant_A = (A[1,1] * ((A[2,2] * A[3,3]) - (A[3,2] * A[2,3]))) - (A[1,2] * ((A[2,1] * A[3,3])-(A[3,1]*A[2,3]))) + (A[1,3] * ((A[2,1] * A[3,2]) - (A[3,1] * A[2,2])))

determinant_A
## [1] 60