library(matlib)C <- matrix(c(0, -1, 1, 0, 1, 2, 3, 1, 3, -2, 4, 0, -3, 0, 4, -6), 4, 4)
d <- c(1, 3, 6, -2)
C## [,1] [,2] [,3] [,4]
## [1,] 0 1 3 -3
## [2,] -1 2 -2 0
## [3,] 1 3 4 4
## [4,] 0 1 0 -6d## [1] 1 3 6 -2showEqn(C, d)## 0*x1 + 1*x2 + 3*x3 - 3*x4 = 1
## -1*x1 + 2*x2 - 2*x3 + 0*x4 = 3
## 1*x1 + 3*x2 + 4*x3 + 4*x4 = 6
## 0*x1 + 1*x2 + 0*x3 - 6*x4 = -2echelon(C, d, verbose=TRUE, fractions=TRUE)##
## Initial matrix:
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 1 3 -3 1
## [2,] -1 2 -2 0 3
## [3,] 1 3 4 4 6
## [4,] 0 1 0 -6 -2
##
## row: 1
##
## exchange rows 1 and 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] -1 2 -2 0 3
## [2,] 0 1 3 -3 1
## [3,] 1 3 4 4 6
## [4,] 0 1 0 -6 -2
##
## multiply row 1 by -1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 -2 2 0 -3
## [2,] 0 1 3 -3 1
## [3,] 1 3 4 4 6
## [4,] 0 1 0 -6 -2
##
## subtract row 1 from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 -2 2 0 -3
## [2,] 0 1 3 -3 1
## [3,] 0 5 2 4 9
## [4,] 0 1 0 -6 -2
##
## row: 2
##
## exchange rows 2 and 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 -2 2 0 -3
## [2,] 0 5 2 4 9
## [3,] 0 1 3 -3 1
## [4,] 0 1 0 -6 -2
##
## multiply row 2 by 1/5
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 -2 2 0 -3
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 1 3 -3 1
## [4,] 0 1 0 -6 -2
##
## multiply row 2 by 2 and add to row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 14/5 8/5 3/5
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 1 3 -3 1
## [4,] 0 1 0 -6 -2
##
## subtract row 2 from row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 14/5 8/5 3/5
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 0 13/5 -19/5 -4/5
## [4,] 0 1 0 -6 -2
##
## subtract row 2 from row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 14/5 8/5 3/5
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 0 13/5 -19/5 -4/5
## [4,] 0 0 -2/5 -34/5 -19/5
##
## row: 3
##
## multiply row 3 by 5/13
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 14/5 8/5 3/5
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 -2/5 -34/5 -19/5
##
## multiply row 3 by 14/5 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 74/13 19/13
## [2,] 0 1 2/5 4/5 9/5
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 -2/5 -34/5 -19/5
##
## multiply row 3 by 2/5 and subtract from row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 74/13 19/13
## [2,] 0 1 0 18/13 25/13
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 -2/5 -34/5 -19/5
##
## multiply row 3 by 2/5 and add to row 4
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 74/13 19/13
## [2,] 0 1 0 18/13 25/13
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 0 -96/13 -51/13
##
## row: 4
##
## multiply row 4 by -13/96
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 74/13 19/13
## [2,] 0 1 0 18/13 25/13
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 0 1 17/32
##
## multiply row 4 by 74/13 and subtract from row 1
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 -25/16
## [2,] 0 1 0 18/13 25/13
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 0 1 17/32
##
## multiply row 4 by 18/13 and subtract from row 2
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 -25/16
## [2,] 0 1 0 0 19/16
## [3,] 0 0 1 -19/13 -4/13
## [4,] 0 0 0 1 17/32
##
## multiply row 4 by 19/13 and add to row 3
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 0 0 0 -25/16
## [2,] 0 1 0 0 19/16
## [3,] 0 0 1 0 15/32
## [4,] 0 0 0 1 17/32Model linier-Gaussian adalah jaring Bayes di mana semua variabel adalah Gaussian, dan rata-rata setiap variabel adalah linier dalam nilai induknya. banyak digunakan karena mendukung inferensi yang efisien. Sistem dinamik linier adalah kasus khusus yang penting.