Question 1
# assign to the variable a single random integer between 3 and 10 using sample function
n_dims <- sample(3:10, 1)
print(n_dims)## [1] 7# create a vector of consecutive integers 1:n_dims^2
my_vec <- 1:n_dims^2
print(my_vec)## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49# use the sample matrix to reshuffle these values
my_vec <- sample(my_vec)
print(my_vec)## [1] 42 37 12 23 27 49 44 38 39 45 47 6 5 21 34 30 17 13 11 41 7 24 35 48 26
## [26] 40 1 22 19 33 25 10 46 9 3 18 36 2 31 16 8 20 15 32 14 4 29 43 28# create a square matrix with these elements and print matrix
my_matrix <- matrix(data=(my_vec^2), nrow = n_dims, ncol = n_dims)
print(my_matrix)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1764 1444 1156 576 361 324 225
## [2,] 1369 1521 900 1225 1089 1296 1024
## [3,] 144 2025 289 2304 625 4 196
## [4,] 529 2209 169 676 100 961 16
## [5,] 729 36 121 1600 2116 256 841
## [6,] 2401 25 1681 1 81 64 1849
## [7,] 1936 441 49 484 9 400 784# find a function in r to transpose the matrix and print again (it worked! it transposed the matrix!)
transpose_matrix <- t(my_matrix)
print(transpose_matrix)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1764 1369 144 529 729 2401 1936
## [2,] 1444 1521 2025 2209 36 25 441
## [3,] 1156 900 289 169 121 1681 49
## [4,] 576 1225 2304 676 1600 1 484
## [5,] 361 1089 625 100 2116 81 9
## [6,] 324 1296 4 961 256 64 400
## [7,] 225 1024 196 16 841 1849 784# calculate the sum and the mean of the elements in the first row and then the last row
sum_first_row <- sum(transpose_matrix[1, ])
print(sum_first_row)## [1] 8872mean_first_row <- mean(transpose_matrix[1,])
print(mean_first_row)## [1] 1267.429sum_last_row <- sum(transpose_matrix[n_dims, ])
print(sum_last_row)## [1] 4935mean_last_row <- mean(transpose_matrix[n_dims, ])
print(mean_last_row)## [1] 705# use eigen() function on matrix
eigen_matrix <- eigen(transpose_matrix)
print(eigen_matrix)## eigen() decomposition
## $values
## [1] 5994.6220+ 0.000i -473.5709+1412.036i -473.5709-1412.036i
## [4] 582.5589+1255.940i 582.5589-1255.940i 1345.9267+ 0.000i
## [7] -344.5248+ 0.000i
##
## $vectors
## [,1] [,2] [,3]
## [1,] 0.5328776+0i -0.160200678+0.22643244i -0.160200678-0.22643244i
## [2,] 0.5282673+0i 0.511548232+0.00000000i 0.511548232+0.00000000i
## [3,] 0.2815041+0i -0.293514111-0.20468786i -0.293514111+0.20468786i
## [4,] 0.4035281+0i 0.008453165+0.37603443i 0.008453165-0.37603443i
## [5,] 0.2592958+0i -0.102806096-0.04191433i -0.102806096+0.04191433i
## [6,] 0.2392229+0i 0.162046334-0.34349011i 0.162046334+0.34349011i
## [7,] 0.2653935+0i -0.484459249-0.02429728i -0.484459249+0.02429728i
## [,4] [,5] [,6]
## [1,] 0.6790722+0.00000000i 0.6790722+0.00000000i -0.08309610+0i
## [2,] -0.2582552-0.33310117i -0.2582552+0.33310117i 0.44551166+0i
## [3,] 0.0154577-0.14268990i 0.0154577+0.14268990i 0.29069203+0i
## [4,] -0.1752524+0.03324724i -0.1752524-0.03324724i -0.22375550+0i
## [5,] -0.1156310+0.18811843i -0.1156310-0.18811843i -0.80605670+0i
## [6,] -0.1964457+0.13529193i -0.1964457-0.13529193i 0.08358981+0i
## [7,] 0.1021236+0.43898472i 0.1021236-0.43898472i -0.05771797+0i
## [,7]
## [1,] -0.08382407+0i
## [2,] -0.57307892+0i
## [3,] -0.11171768+0i
## [4,] 0.66905373+0i
## [5,] 0.25704489+0i
## [6,] 0.32602659+0i
## [7,] -0.17909477+0i# $values and $vectors- what kinds of numbers are these?
##### outputs are complex numbers for square matrices
#figure out their data type
typeof(eigen_matrix)## [1] "list"Question 2
# my_matrix: 4x4 matrix with random uniform values between 0 and 1
my_matrix = matrix(runif(16), nrow = 4, ncol = 4)
print(my_matrix)## [,1] [,2] [,3] [,4]
## [1,] 0.74324903 0.8712035 0.629364799 0.86696385
## [2,] 0.08410895 0.7308486 0.283997210 0.08975908
## [3,] 0.73162592 0.7156768 0.005349946 0.14198044
## [4,] 0.53803465 0.6242206 0.584260358 0.71076866# my_logical: 100-element vector of TRUE/FALSE values and then assign some inequality (0.5)
my_logical = runif(100) > 0.5
print(my_logical)## [1] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## [13] TRUE FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE
## [25] TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE TRUE
## [37] FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE
## [61] TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE
## [85] TRUE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE
## [97] TRUE TRUE TRUE TRUE# my_letters: 26-element vector with all lowercase letters in random order
my_letters = sample(letters, 26)
print(my_letters)## [1] "j" "o" "a" "i" "l" "u" "x" "f" "z" "n" "s" "m" "q" "k" "h" "t" "d" "g" "b"
## [20] "y" "w" "c" "r" "p" "v" "e"# create list
my_list <- list(my_matrix, my_logical, my_letters)
# print the list
print(my_list)## [[1]]
## [,1] [,2] [,3] [,4]
## [1,] 0.74324903 0.8712035 0.629364799 0.86696385
## [2,] 0.08410895 0.7308486 0.283997210 0.08975908
## [3,] 0.73162592 0.7156768 0.005349946 0.14198044
## [4,] 0.53803465 0.6242206 0.584260358 0.71076866
##
## [[2]]
## [1] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
## [13] TRUE FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE
## [25] TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE TRUE
## [37] FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE
## [49] FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE
## [61] TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE FALSE
## [73] FALSE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE
## [85] TRUE FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE
## [97] TRUE TRUE TRUE TRUE
##
## [[3]]
## [1] "j" "o" "a" "i" "l" "u" "x" "f" "z" "n" "s" "m" "q" "k" "h" "t" "d" "g" "b"
## [20] "y" "w" "c" "r" "p" "v" "e"# Using the original list (my_list)
my_matrix_list <- my_matrix[2,2]
my_logical_list <- my_logical[2]
my_letters_list <- my_letters[2]
# create new list
new_list <- list(my_matrix_list,my_logical_list,my_letters_list)
print(new_list)## [[1]]
## [1] 0.7308486
##
## [[2]]
## [1] FALSE
##
## [[3]]
## [1] "o"# Check the types of each component in the new list
typeof(new_list[[1]]) ## [1] "double"typeof(new_list[[2]]) ## [1] "logical"typeof(new_list[[3]]) ## [1] "character"# Combine the elements into a single atomic vector
combined_vector <- c(my_matrix_list, my_logical_list, my_letters_list)
# Check the data type of the combined vector
typeof(combined_vector)## [1] "character"Question 3
# defining my_unis
my_unis_10 <- sample(0:10)
my_unis_20 <- sample(0:10)
my_unis_26 <- sample(0:10, 4)
my_unis <- c(my_unis_10,my_unis_20,my_unis_26)
print(my_unis)## [1] 3 0 7 9 8 10 5 2 1 4 6 0 4 10 2 3 8 7 1 9 5 6 4 3 8
## [26] 9# defining my_letters
my_letters <- sample(LETTERS, 26)
print(my_letters)## [1] "S" "W" "H" "L" "O" "A" "J" "G" "F" "N" "T" "R" "P" "I" "Q" "B" "Z" "E" "M"
## [20] "U" "Y" "X" "K" "D" "C" "V"# create data frame
my_df <- data.frame(my_unis,my_letters)
print(my_df)## my_unis my_letters
## 1 3 S
## 2 0 W
## 3 7 H
## 4 9 L
## 5 8 O
## 6 10 A
## 7 5 J
## 8 2 G
## 9 1 F
## 10 4 N
## 11 6 T
## 12 0 R
## 13 4 P
## 14 10 I
## 15 2 Q
## 16 3 B
## 17 8 Z
## 18 7 E
## 19 1 M
## 20 9 U
## 21 5 Y
## 22 6 X
## 23 4 K
## 24 3 D
## 25 8 C
## 26 9 V# for the first variable, use a single line of code in R to select 4 random rows and replace the numerical values in those rows with NA
my_df$my_unis[sample(1:nrow(my_df), 4)] <- NA
print(my_df)## my_unis my_letters
## 1 3 S
## 2 0 W
## 3 7 H
## 4 9 L
## 5 8 O
## 6 10 A
## 7 5 J
## 8 2 G
## 9 NA F
## 10 4 N
## 11 NA T
## 12 0 R
## 13 4 P
## 14 10 I
## 15 2 Q
## 16 3 B
## 17 8 Z
## 18 7 E
## 19 1 M
## 20 9 U
## 21 5 Y
## 22 6 X
## 23 NA K
## 24 3 D
## 25 8 C
## 26 NA V# for the first variable, write a single line of R code to identify which rows have the missing values
which(!complete.cases(my_df$my_unis))## [1] 9 11 23 26# reorder the entire data frame to arrange the second variable in alphabetical order
my_df <- my_df[order(my_df$my_letters), ]
print(my_df)## my_unis my_letters
## 6 10 A
## 16 3 B
## 25 8 C
## 24 3 D
## 18 7 E
## 9 NA F
## 8 2 G
## 3 7 H
## 14 10 I
## 7 5 J
## 23 NA K
## 4 9 L
## 19 1 M
## 10 4 N
## 5 8 O
## 13 4 P
## 15 2 Q
## 12 0 R
## 1 3 S
## 11 NA T
## 20 9 U
## 26 NA V
## 2 0 W
## 22 6 X
## 21 5 Y
## 17 8 Z# calculate the column mean for the first variable
mean_my_unis <- mean(my_df$my_unis, na.rm =TRUE)
print(mean_my_unis)## [1] 5.181818