Diadopsi dari website https://rpubs.com/michaelmallari/linear-algebra-for-data-science

Membuat Vector di R

Aljabar Linear untuk Sains Data Membuat Vektor Data :

rep(3, 3)
## [1] 3 3 3
rep(4, 4)
## [1] 4 4 4 4

Membuat vektor bilangan genap dan ganjil

seq(2, 6, by = 2)
## [1] 2 4 6
seq(1, 5, by = 2)
## [1] 1 3 5

Menampilkan data vektor di atas menggunakan 'c'

c(3, 3, 3)
## [1] 3 3 3
c(4, 4, 4, 4)
## [1] 4 4 4 4
c(2, 4, 6)
## [1] 2 4 6
c(1, 3, 5)
## [1] 1 3 5

Aljabar dalam Vectors

x=c(1,2,3)
y=seq(2, 6, by = 2)
z=rep(2, 3)
#Penjumlahan x dan y dan cetak
print(x + y)
## [1] 3 6 9
# Multiply z by 2 and print
print(2*z)
## [1] 4 4 4
# Multiply x and y by each other and print
print(x*y)
## [1]  2  8 18
# Add x to z, if possible, and print
print(x + z)
## [1] 3 4 5

Membuat Matrik di R

#membuat matriks 3 kolom dan 2 baris yang berisi bilangan 1 
matrix(1, nrow = 2, ncol = 3)
##      [,1] [,2] [,3]
## [1,]    1    1    1
## [2,]    1    1    1
print(matrix(2, nrow = 3, ncol = 2))
##      [,1] [,2]
## [1,]    2    2
## [2,]    2    2
## [3,]    2    2
# Membuat Matriks, mengubah fungsinya dengan byrow.
B <- matrix(c(1, 2, 3, 2), nrow = 2, ncol = 2, byrow = FALSE)
A <- matrix(c(1, 2, 3, 2), nrow = 2, ncol = 2, byrow = TRUE)

# Menjumlahkan A dengan matriks yang telah dibuat sebelumnya
A + B
##      [,1] [,2]
## [1,]    2    5
## [2,]    5    4

Operasi Vector - Matriks

 A = matrix(c(1, 2, 3, -1, 0, 3), nrow = 2, ncol = 3, byrow = TRUE)
b = c(-2, 2, 2)

# Kalikan A dan b
A%*%b
##      [,1]
## [1,]    8
## [2,]    8

Pentingnya Urutan dalam Perkalian Matriks

A = matrix(c(1, 3, 2, -1), nrow = 2, ncol = 2)
B = matrix(c(-1, 1, 2, -3), nrow = 2, ncol = 2)
b = c(-2, 2)

# Kalikan A dan B
A%*%B
##      [,1] [,2]
## [1,]    1   -4
## [2,]   -4    9
# Kalikan hasil A dan B dengan b
A%*%B%*%b
##      [,1]
## [1,]  -10
## [2,]   26
# Multiply A on the right of B, and then by the vector b
B%*%A%*%b
##      [,1]
## [1,]  -18
## [2,]   26

Intro to The Matrix Inverse

# Take the inverse of the 2 by 2 identity matrix
solve(diag(2))
##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1
# Take the inverse of the matrix A
Ainv <- solve(A)

# Multiply A inverse by A
Ainv%*%A
##      [,1]          [,2]
## [1,]    1 -5.551115e-17
## [2,]    0  1.000000e+00
# Multiply A by its inverse
A%*%Ainv
##      [,1]         [,2]
## [1,]    1 5.551115e-17
## [2,]    0 1.000000e+00