Data605-Week4-Discussion4-kamath

Exercise- Representations- C10

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#defining the matrix B and v:
B <- matrix(c(2, -2, 2, 1, 3, 1, 3, 5, 2), 3, 3)
B

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

v <- matrix(c(11, 5, 8), 3, 1)
v

##      [,1]
## [1,]   11
## [2,]    5
## [3,]    8

# With augmented matrix we have as below:
A <- matrix(c(2, -2, 2, 1, 3, 1, 3, 5, 2, 11, 5, 8), 3, 4)
A

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

Arref <- pracma::rref(A)
Arref

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

pB.v <- matrix(Arref[,4 ], 3, 1)
pB.v

##      [,1]
## [1,]    2
## [2,]   -2
## [3,]    3

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