Exercise LISS.C20 Robert Beezer

  • I have intentionally attempted to use the terms from the textbook, to see if I am understanding them correctly(trivial,homogeneous etc..). If anyone see’s I misused them please let me know.

  • In the vector space of 2×2matrices, M22, determine if the sets below is linearly independent. Caption for the picture.

  • Solve set of equations and determine if the only solution is trivial solution(reduce row echelon form is identity matrix/ zero vector is our only solution set)
    • Setup equations from matrices and set equations =0 to solve for homogeneous solution/s \[2x+0y+4z=0\] \[-x+4y+2z=0\] \[ x-y+z=0\] \[3x+2y+3z=0\]

Build matrix in R from set of equations and solve for RREF

library(pracma)

my_matrix <- matrix(c(2,-1,1,3,0,4,-1,2,4,2,1,3,0,0,0,0),nrow=4)
rref(my_matrix)
##      [,1] [,2] [,3] [,4]
## [1,]    1    0    0    0
## [2,]    0    1    0    0
## [3,]    0    0    1    0
## [4,]    0    0    0    0
#solve(my_matrix)
det(my_matrix)
## [1] 0
  • As the reduced row echelon form is the identity matrix, the set is linearly independent.