library(matlib)## Warning: package 'matlib' was built under R version 4.2.3A <- matrix(c(9,-2,3,4,6,-4,6,-2,5,-3,9,-1,6,-7,2,-4),4,4)
B <- c(4,6,3,6)
A## [,1] [,2] [,3] [,4]
## [1,] 9 6 5 6
## [2,] -2 -4 -3 -7
## [3,] 3 6 9 2
## [4,] 4 -2 -1 -4B## [1] 4 6 3 6showEqn(A,B)## 9*x1 + 6*x2 + 5*x3 + 6*x4 = 4
## -2*x1 - 4*x2 - 3*x3 - 7*x4 = 6
## 3*x1 + 6*x2 + 9*x3 + 2*x4 = 3
## 4*x1 - 2*x2 - 1*x3 - 4*x4 = 6Model linear-Gaussian adalah jaringan Bayes dimana semua variabel adalah Gaussian, dan rata-rata setiap variabel adalah linear dalam nilai induknya. Banyak digunakan karena mendukung inferensi yang efisien. Sistem dinamik linear adalah kasus Khusus yang penting
echelon(A, B, verbose=TRUE, fractions=TRUE)##
## Initial matrix:
## [,1] [,2] [,3] [,4] [,5]
## [1,] 9 6 5 6 4
## [2,] -2 -4 -3 -7 6
## [3,] 3 6 9 2 3
## [4,] 4 -2 -1 -4 6
##
## row: 1
##
## multiply row 1 by 1/9
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] -2 -4 -3 -7 6
## [3,] 3 6 9 2 3
## [4,] 4 -2 -1 -4 6
##
## multiply row 1 by 2 and add to row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] 0 -8/3 -17/9 -17/3 62/9
## [3,] 3 6 9 2 3
## [4,] 4 -2 -1 -4 6
##
## multiply row 1 by 3 and subtract from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] 0 -8/3 -17/9 -17/3 62/9
## [3,] 0 4 22/3 0 5/3
## [4,] 4 -2 -1 -4 6
##
## multiply row 1 by 4 and subtract from row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] 0 -8/3 -17/9 -17/3 62/9
## [3,] 0 4 22/3 0 5/3
## [4,] 0 -14/3 -29/9 -20/3 38/9
##
## row: 2
##
## exchange rows 2 and 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] 0 -14/3 -29/9 -20/3 38/9
## [3,] 0 4 22/3 0 5/3
## [4,] 0 -8/3 -17/9 -17/3 62/9
##
## multiply row 2 by -3/14
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2/3 5/9 2/3 4/9
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 4 22/3 0 5/3
## [4,] 0 -8/3 -17/9 -17/3 62/9
##
## multiply row 2 by 2/3 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 2/21 -2/7 22/21
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 4 22/3 0 5/3
## [4,] 0 -8/3 -17/9 -17/3 62/9
##
## multiply row 2 by 4 and subtract from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 2/21 -2/7 22/21
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 0 32/7 -40/7 37/7
## [4,] 0 -8/3 -17/9 -17/3 62/9
##
## multiply row 2 by 8/3 and add to row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 2/21 -2/7 22/21
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 0 32/7 -40/7 37/7
## [4,] 0 0 -1/21 -13/7 94/21
##
## row: 3
##
## multiply row 3 by 7/32
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 2/21 -2/7 22/21
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 -1/21 -13/7 94/21
##
## multiply row 3 by 2/21 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -1/6 15/16
## [2,] 0 1 29/42 10/7 -19/21
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 -1/21 -13/7 94/21
##
## multiply row 3 by 29/42 and subtract from row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -1/6 15/16
## [2,] 0 1 0 55/24 -109/64
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 -1/21 -13/7 94/21
##
## multiply row 3 by 1/21 and add to row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -1/6 15/16
## [2,] 0 1 0 55/24 -109/64
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 0 -23/12 145/32
##
## row: 4
##
## multiply row 4 by -12/23
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 -1/6 15/16
## [2,] 0 1 0 55/24 -109/64
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 0 1 -435/184
##
## multiply row 4 by 1/6 and add to row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 25/46
## [2,] 0 1 0 55/24 -109/64
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 0 1 -435/184
##
## multiply row 4 by 55/24 and subtract from row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 25/46
## [2,] 0 1 0 0 1367/368
## [3,] 0 0 1 -5/4 37/32
## [4,] 0 0 0 1 -435/184
##
## multiply row 4 by 5/4 and add to row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 25/46
## [2,] 0 1 0 0 1367/368
## [3,] 0 0 1 0 -331/184
## [4,] 0 0 0 1 -435/184