library(pracma)
## Warning: package 'pracma' was built under R version 4.3.2

#C26. p.278: Doing the computations by hand, find the determinant of the matrix A.

A <- matrix(c(2,0,3,2,5,1,2,4,3,0,1,2,5,3,2,1), nrow = 4, byrow = T)
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
determinant_A <- det(A)
determinant_A
## [1] 29

##Without the use of the det() function the math steps for this determinant would take awhile. Since the lower left triangle is not filled with 6 zeros, multiplication across the diagonal row will not yield the correct determinant. The 4X4 matrix above is also not sparse (meaning more than 2 zeros in the lower triangle), increasing the number of row operations and row swaps needed.