Week 2 Discussion

Page 278 C26

A <- matrix(c(2,0,3,2,
              5,1,2,4,
              3,0,1,2,
              5,3,2,1), nrow = 4, byrow = TRUE)
A

##      [,1] [,2] [,3] [,4]
## [1,]    2    0    3    2
## [2,]    5    1    2    4
## [3,]    3    0    1    2
## [4,]    5    3    2    1

Compute the determinant of A by hand

detA_by_hand <- A[1, 1] * (A[2, 2] * (A[3, 3] * A[4, 4] - A[3, 4] * A[4, 3]) -
                           A[2, 3] * (A[3, 2] * A[4, 4] - A[3, 4] * A[4, 2]) +
                           A[2, 4] * (A[3, 2] * A[4, 3] - A[3, 3] * A[4, 2])) -
              A[1, 2] * (A[2, 1] * (A[3, 3] * A[4, 4] - A[3, 4] * A[4, 3]) -
                         A[2, 3] * (A[3, 1] * A[4, 4] - A[3, 4] * A[4, 1]) +
                         A[2, 4] * (A[3, 1] * A[4, 3] - A[3, 3] * A[4, 1])) +
              A[1, 3] * (A[2, 1] * (A[3, 2] * A[4, 4] - A[3, 4] * A[4, 2]) -
                         A[2, 2] * (A[3, 1] * A[4, 4] - A[3, 4] * A[4, 1]) +
                         A[2, 4] * (A[3, 1] * A[4, 2] - A[3, 2] * A[4, 1])) -
              A[1, 4] * (A[2, 1] * (A[3, 2] * A[4, 3] - A[3, 3] * A[4, 2]) -
                         A[2, 2] * (A[3, 1] * A[4, 3] - A[3, 3] * A[4, 1]) +
                         A[2, 3] * (A[3, 1] * A[4, 2] - A[3, 2] * A[4, 1]))
detA_by_hand

## [1] 29

Compute using built in R function to validate ansewer

detA_R <- det(A)
detA_R

## [1] 29