Discussion week2

Linear algebra text, Chapters VS, D

Fundamentals of Computational Mathematics

CUNY MSDS DATA 605, Fall 2018

Rose Koh

09/04/2018

Chapter VS Section D Dimension

A <- matrix(c(2,-1,-3,11,9,
              1,2,1,-7,-3,
              3,1,-3,6,8,
              2,1,2,-5,-3), 4, byrow=T)

print(A)

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    2   -1   -3   11    9
## [2,]    1    2    1   -7   -3
## [3,]    3    1   -3    6    8
## [4,]    2    1    2   -5   -3

# row reduce A
library(pracma)
print(rref(A))

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

# r = 3 for A, Then dim(N(A)) = n(A)
# = (n(A) + r(A)) - r(A)
# = 5 - r(A)        (Theorem RPNC said that the rank and nullity of a matrix sum to the number of columns of the matrix)
# = 5 - 3           (Theorem CRN)
# = 2

• reference