NAMA : MUHAMMAD FAQIH
KELAS : LINEAR ALGEBRA B
DOSEN PENGAMPU Prof. Dr. Suhartono, M. Kom
library(matlib)## Warning: package 'matlib' was built under R version 4.2.2Membuat sebuah matriks 4x4 dengan isi elemen yang sudah ditentukan pada parameter pertama dari fungsi “matrix()”, dan membuat sebuah vektor dengan isi elemen yang sudah ditentukan pada variabel “b”.
A <- matrix(c(8, -3, 6, 9, 1, 1, 0, 1, 3, -4, 2, 0, -1, 0, 4, -4), 4, 4)
b <- c(1, 1, 5, -2)Tampilkan Persamaan matriks a dan vektor b
showEqn(A, b)## 8*x1 + 1*x2 + 3*x3 - 1*x4 = 1
## -3*x1 + 1*x2 - 4*x3 + 0*x4 = 1
## 6*x1 + 0*x2 + 2*x3 + 4*x4 = 5
## 9*x1 + 1*x2 + 0*x3 - 4*x4 = -2echelon(A, b, verbose=TRUE, fractions=TRUE)##
## Initial matrix:
## [,1] [,2] [,3] [,4] [,5]
## [1,] 8 1 3 -1 1
## [2,] -3 1 -4 0 1
## [3,] 6 0 2 4 5
## [4,] 9 1 0 -4 -2
##
## row: 1
##
## exchange rows 1 and 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9 1 0 -4 -2
## [2,] -3 1 -4 0 1
## [3,] 6 0 2 4 5
## [4,] 8 1 3 -1 1
##
## multiply row 1 by 1/9
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1/9 0 -4/9 -2/9
## [2,] -3 1 -4 0 1
## [3,] 6 0 2 4 5
## [4,] 8 1 3 -1 1
##
## multiply row 1 by 3 and add to row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1/9 0 -4/9 -2/9
## [2,] 0 4/3 -4 -4/3 1/3
## [3,] 6 0 2 4 5
## [4,] 8 1 3 -1 1
##
## multiply row 1 by 6 and subtract from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1/9 0 -4/9 -2/9
## [2,] 0 4/3 -4 -4/3 1/3
## [3,] 0 -2/3 2 20/3 19/3
## [4,] 8 1 3 -1 1
##
## multiply row 1 by 8 and subtract from row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1/9 0 -4/9 -2/9
## [2,] 0 4/3 -4 -4/3 1/3
## [3,] 0 -2/3 2 20/3 19/3
## [4,] 0 1/9 3 23/9 25/9
##
## row: 2
##
## multiply row 2 by 3/4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 1/9 0 -4/9 -2/9
## [2,] 0 1 -3 -1 1/4
## [3,] 0 -2/3 2 20/3 19/3
## [4,] 0 1/9 3 23/9 25/9
##
## multiply row 2 by 1/9 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 1/3 -1/3 -1/4
## [2,] 0 1 -3 -1 1/4
## [3,] 0 -2/3 2 20/3 19/3
## [4,] 0 1/9 3 23/9 25/9
##
## multiply row 2 by 2/3 and add to row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 1/3 -1/3 -1/4
## [2,] 0 1 -3 -1 1/4
## [3,] 0 0 0 6 13/2
## [4,] 0 1/9 3 23/9 25/9
##
## multiply row 2 by 1/9 and subtract from row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 1/3 -1/3 -1/4
## [2,] 0 1 -3 -1 1/4
## [3,] 0 0 0 6 13/2
## [4,] 0 0 10/3 8/3 11/4
##
## row: 3
##
## exchange rows 3 and 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 1/3 -1/3 -1/4
## [2,] 0 1 -3 -1 1/4
## [3,] 0 0 10/3 8/3 11/4
## [4,] 0 0 0 6 13/2
##
## multiply row 3 by 3/10
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 1/3 -1/3 -1/4
## [2,] 0 1 -3 -1 1/4
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 6 13/2
##
## multiply row 3 by 1/3 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -3/5 -21/40
## [2,] 0 1 -3 -1 1/4
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 6 13/2
##
## multiply row 3 by 3 and add to row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -3/5 -21/40
## [2,] 0 1 0 7/5 109/40
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 6 13/2
##
## row: 4
##
## multiply row 4 by 1/6
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -3/5 -21/40
## [2,] 0 1 0 7/5 109/40
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 1 13/12
##
## multiply row 4 by 3/5 and add to row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 1/8
## [2,] 0 1 0 7/5 109/40
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 1 13/12
##
## multiply row 4 by 7/5 and subtract from row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 1/8
## [2,] 0 1 0 0 29/24
## [3,] 0 0 1 4/5 33/40
## [4,] 0 0 0 1 13/12
##
## multiply row 4 by 4/5 and subtract from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 1/8
## [2,] 0 1 0 0 29/24
## [3,] 0 0 1 0 -1/24
## [4,] 0 0 0 1 13/12Transformasi matriks A dan vektor b ke dalam bentuk matriks eselon. Dalam bentuk matriks eselon, setiap baris nol pada matriks A diletakkan di bawah baris yang berisi elemen bukan nol dan setiap elemen nol pada kolom k berada di bawah elemen pada baris k yang memiliki elemen bukan nol.