HELLO!

Teknik Informatika UIN MAULANA MALIK IBRAHIM MALANG|| Lalu Egiq Fahalik Anggara_220605110066 | linier algebra

by Prof. Dr. Suhartono, M.Kom

library(mvtnorm)
library(ggplot2)
library(matlib)
## Warning: package 'matlib' was built under R version 4.2.3
v1 <- c(2, -1, 3)
v1
## [1]  2 -1  3
v2 <- c(-1, 0, 4)
v2
## [1] -1  0  4
v1 + v2
## [1]  1 -1  7
A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)
A
##      [,1] [,2] [,3]
## [1,]    3    0   -5
## [2,]   -1   -3    4
B <- matrix(c(-5, 5, 2, 1, -2, 0), nrow = 2, ncol = 3, byrow = TRUE)
B
##      [,1] [,2] [,3]
## [1,]   -5    5    2
## [2,]    1   -2    0
A+B
##      [,1] [,2] [,3]
## [1,]   -2    5   -3
## [2,]    0   -5    4
A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)
A
##      [,1] [,2] [,3]
## [1,]    3    0   -5
## [2,]   -1   -3    4
-3*A
##      [,1] [,2] [,3]
## [1,]   -9    0   15
## [2,]    3    9  -12
3*A
##      [,1] [,2] [,3]
## [1,]    9    0  -15
## [2,]   -3   -9   12
2*A
##      [,1] [,2] [,3]
## [1,]    6    0  -10
## [2,]   -2   -6    8
v1 <- c(2, -1, 3)
v2 <- c(-1, 0, 4)
v1
## [1]  2 -1  3
v2
## [1] -1  0  4
v1%*%v2
##      [,1]
## [1,]   10
A <- matrix(c(3, 0, -5, -1, -3, 4), nrow = 2, ncol = 3, byrow = TRUE)
B <- matrix(c(-5, 5, 2, 1, -2, 0), nrow = 3, ncol = 2, byrow = TRUE)
A
##      [,1] [,2] [,3]
## [1,]    3    0   -5
## [2,]   -1   -3    4
B
##      [,1] [,2]
## [1,]   -5    5
## [2,]    2    1
## [3,]   -2    0
A %*% B
##      [,1] [,2]
## [1,]   -5   15
## [2,]   -9   -8
A <- matrix(c(4, -1, -5, 0, 1, -2), 2, 3, byrow = TRUE)
t(A)
##      [,1] [,2]
## [1,]    4    0
## [2,]   -1    1
## [3,]   -5   -2
## Standard deviation
sigma <- matrix(c(4,2,2,3), ncol = 2, nrow = 2)
sigma
##      [,1] [,2]
## [1,]    4    2
## [2,]    2    3
## Mean
mu <- c(1, 2)
mu
## [1] 1 2
n<-100

n
## [1] 100
set.seed(123)
library(matlib)
A <- matrix(c(1, 3, 2, 1, 2, 5, -2, -3, 2, 2, -3, -3,
-4, -2, -1, 4), nrow = 4, ncol = 4, byrow=TRUE)
#Then we create a matrix M with the function diag():
M <- cbind(A, diag(4))
#Now we upload the pracma package.
library(pracma)
## Warning: package 'pracma' was built under R version 4.2.3
## 
## Attaching package: 'pracma'
## The following objects are masked from 'package:matlib':
## 
##     angle, inv
R <- rref(M)
#If you want to obtain the inverse of the matrix A, then we take the fifth, sixth, seventh and eighth columns of R.
Ainv <- R[, 5:8]
Ainv
##             [,1]       [,2]       [,3]        [,4]
## [1,]  0.58024691 -0.7037037  0.8641975 -0.02469136
## [2,]  0.04938272  0.2592593 -0.1604938  0.06172840
## [3,] -0.14814815  0.2222222 -0.5185185 -0.18518519
## [4,]  0.56790123 -0.5185185  0.6543210  0.20987654
A <- matrix(runif(25), 5, 5)
A <- matrix(sample(-100:100, 25, replace=TRUE), 5, 5)
A
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   -2   36    2    8  -78
## [2,]  -29   63   16  -94   54
## [3,]  -75  -23  -25   36   87
## [4,]  -94  -20   42   68  -48
## [5,]   69  -58  -69  -27   34
A <- matrix(c(1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 0 ,
0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 0 ,
0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 ,
0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ,
0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ,
0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,
1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 ,
0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ,
1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 ,
0 , 0 , 0 , 0 , 0 , 1), nrow = 11, ncol = 18, byrow = TRUE)
A
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
##  [1,]    1    1    1    1    1    1    1    1    1     0     0     0     0
##  [2,]    0    0    0    0    0    0    0    0    0     1     1     1     1
##  [3,]    1    0    0    0    0    0    0    0    0     1     0     0     0
##  [4,]    0    1    0    0    0    0    0    0    0     0     1     0     0
##  [5,]    0    0    1    0    0    0    0    0    0     0     0     1     0
##  [6,]    0    0    0    1    0    0    0    0    0     0     0     0     1
##  [7,]    0    0    0    0    1    0    0    0    0     0     0     0     0
##  [8,]    0    0    0    0    0    1    0    0    0     0     0     0     0
##  [9,]    0    0    0    0    0    0    1    0    0     0     0     0     0
## [10,]    0    0    0    0    0    0    0    1    0     0     0     0     0
## [11,]    0    0    0    0    0    0    0    0    1     0     0     0     0
##       [,14] [,15] [,16] [,17] [,18]
##  [1,]     0     0     0     0     0
##  [2,]     1     1     1     1     1
##  [3,]     0     0     0     0     0
##  [4,]     0     0     0     0     0
##  [5,]     0     0     0     0     0
##  [6,]     0     0     0     0     0
##  [7,]     1     0     0     0     0
##  [8,]     0     1     0     0     0
##  [9,]     0     0     1     0     0
## [10,]     0     0     0     1     0
## [11,]     0     0     0     0     1
b <- c(1298, 1948, 465, 605, 451, 338, 260, 183, 282, 127, 535)
b
##  [1] 1298 1948  465  605  451  338  260  183  282  127  535
C <- cbind(A, b)
C
##                                              b
##  [1,] 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1298
##  [2,] 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1948
##  [3,] 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0  465
##  [4,] 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0  605
##  [5,] 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0  451
##  [6,] 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0  338
##  [7,] 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0  260
##  [8,] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0  183
##  [9,] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0  282
## [10,] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0  127
## [11,] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1  535
library(pracma)
E <- rref(C)
E*6
##                                                       b
##  [1,] 6 0 0 0 0 0 0 0 0 0 -6 -6 -6 -6 -6 -6 -6 -6 -8898
##  [2,] 0 6 0 0 0 0 0 0 0 0  6  0  0  0  0  0  0  0  3630
##  [3,] 0 0 6 0 0 0 0 0 0 0  0  6  0  0  0  0  0  0  2706
##  [4,] 0 0 0 6 0 0 0 0 0 0  0  0  6  0  0  0  0  0  2028
##  [5,] 0 0 0 0 6 0 0 0 0 0  0  0  0  6  0  0  0  0  1560
##  [6,] 0 0 0 0 0 6 0 0 0 0  0  0  0  0  6  0  0  0  1098
##  [7,] 0 0 0 0 0 0 6 0 0 0  0  0  0  0  0  6  0  0  1692
##  [8,] 0 0 0 0 0 0 0 6 0 0  0  0  0  0  0  0  6  0   762
##  [9,] 0 0 0 0 0 0 0 0 6 0  0  0  0  0  0  0  0  6  3210
## [10,] 0 0 0 0 0 0 0 0 0 6  6  6  6  6  6  6  6  6 11688
## [11,] 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0     0
G1 <- eye(8)
G1
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,]    1    0    0    0    0    0    0    0
## [2,]    0    1    0    0    0    0    0    0
## [3,]    0    0    1    0    0    0    0    0
## [4,]    0    0    0    1    0    0    0    0
## [5,]    0    0    0    0    1    0    0    0
## [6,]    0    0    0    0    0    1    0    0
## [7,]    0    0    0    0    0    0    1    0
## [8,]    0    0    0    0    0    0    0    1
G2 <- matrix(rep(0, 80), 8, 10)
G2
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,]    0    0    0    0    0    0    0    0    0     0
## [2,]    0    0    0    0    0    0    0    0    0     0
## [3,]    0    0    0    0    0    0    0    0    0     0
## [4,]    0    0    0    0    0    0    0    0    0     0
## [5,]    0    0    0    0    0    0    0    0    0     0
## [6,]    0    0    0    0    0    0    0    0    0     0
## [7,]    0    0    0    0    0    0    0    0    0     0
## [8,]    0    0    0    0    0    0    0    0    0     0
b2 <- c(266, 223, 140, 264, 137, 67, 130, 24)
b2
## [1] 266 223 140 264 137  67 130  24
G <- cbind(G1, G2, b2)
G
##                                           b2
## [1,] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 266
## [2,] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 223
## [3,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 140
## [4,] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 264
## [5,] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 137
## [6,] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0  67
## [7,] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 130
## [8,] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0  24
M <- rbind(E, G)
M
##                                                       b
##  [1,] 1 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1483
##  [2,] 0 1 0 0 0 0 0 0 0 0  1  0  0  0  0  0  0  0   605
##  [3,] 0 0 1 0 0 0 0 0 0 0  0  1  0  0  0  0  0  0   451
##  [4,] 0 0 0 1 0 0 0 0 0 0  0  0  1  0  0  0  0  0   338
##  [5,] 0 0 0 0 1 0 0 0 0 0  0  0  0  1  0  0  0  0   260
##  [6,] 0 0 0 0 0 1 0 0 0 0  0  0  0  0  1  0  0  0   183
##  [7,] 0 0 0 0 0 0 1 0 0 0  0  0  0  0  0  1  0  0   282
##  [8,] 0 0 0 0 0 0 0 1 0 0  0  0  0  0  0  0  1  0   127
##  [9,] 0 0 0 0 0 0 0 0 1 0  0  0  0  0  0  0  0  1   535
## [10,] 0 0 0 0 0 0 0 0 0 1  1  1  1  1  1  1  1  1  1948
## [11,] 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0     0
## [12,] 1 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0   266
## [13,] 0 1 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0   223
## [14,] 0 0 1 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0   140
## [15,] 0 0 0 1 0 0 0 0 0 0  0  0  0  0  0  0  0  0   264
## [16,] 0 0 0 0 1 0 0 0 0 0  0  0  0  0  0  0  0  0   137
## [17,] 0 0 0 0 0 1 0 0 0 0  0  0  0  0  0  0  0  0    67
## [18,] 0 0 0 0 0 0 1 0 0 0  0  0  0  0  0  0  0  0   130
## [19,] 0 0 0 0 0 0 0 1 0 0  0  0  0  0  0  0  0  0    24
M2 <- M[,-19]
M2
##                                                  
##  [1,] 1 0 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1
##  [2,] 0 1 0 0 0 0 0 0 0 0  1  0  0  0  0  0  0  0
##  [3,] 0 0 1 0 0 0 0 0 0 0  0  1  0  0  0  0  0  0
##  [4,] 0 0 0 1 0 0 0 0 0 0  0  0  1  0  0  0  0  0
##  [5,] 0 0 0 0 1 0 0 0 0 0  0  0  0  1  0  0  0  0
##  [6,] 0 0 0 0 0 1 0 0 0 0  0  0  0  0  1  0  0  0
##  [7,] 0 0 0 0 0 0 1 0 0 0  0  0  0  0  0  1  0  0
##  [8,] 0 0 0 0 0 0 0 1 0 0  0  0  0  0  0  0  1  0
##  [9,] 0 0 0 0 0 0 0 0 1 0  0  0  0  0  0  0  0  1
## [10,] 0 0 0 0 0 0 0 0 0 1  1  1  1  1  1  1  1  1
## [11,] 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0
## [12,] 1 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0
## [13,] 0 1 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0
## [14,] 0 0 1 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0
## [15,] 0 0 0 1 0 0 0 0 0 0  0  0  0  0  0  0  0  0
## [16,] 0 0 0 0 1 0 0 0 0 0  0  0  0  0  0  0  0  0
## [17,] 0 0 0 0 0 1 0 0 0 0  0  0  0  0  0  0  0  0
## [18,] 0 0 0 0 0 0 1 0 0 0  0  0  0  0  0  0  0  0
## [19,] 0 0 0 0 0 0 0 1 0 0  0  0  0  0  0  0  0  0
M3 <- rref(M2)
M3
##                                          
##  [1,] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [2,] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [3,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [4,] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [5,] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [6,] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
##  [7,] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [8,] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
##  [9,] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## [10,] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [11,] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [12,] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## [13,] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
## [14,] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
## [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

daftar pustaka yoshida, Ruriko.(2021).LINIER ALGEBRA AND ITS APPLICATION WITH R