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# Assign to the variable n_dims a single random integer between 3 and 10.
n_dims <- floor(runif(1, min = 3, max = 10))
print(n_dims)## [1] 5# Create a vector of consecutive integers from 1 to n_dims^2.
next_vector <- seq(1:n_dims^2)
print(next_vector)## [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# Use the sample function to randomly reshuffle these values.
sample(next_vector)## [1] 4 21 5 6 16 11 12 15 22 3 19 20 10 13 7 2 8 25 24 1 14 18 17 23 9# Create a square matrix with these elements.
my_matrix <- matrix(next_vector, nrow = n_dims, byrow = TRUE)
# Print out the matrix.
print(my_matrix)## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2 3 4 5
## [2,] 6 7 8 9 10
## [3,] 11 12 13 14 15
## [4,] 16 17 18 19 20
## [5,] 21 22 23 24 25# Find a function in r to transpose the matrix. I found the function transpose which is t(matrix).
transposed_matrix <- t(my_matrix)
# Print it out again and note how it has changed.
print(transposed_matrix)## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 6 11 16 21
## [2,] 2 7 12 17 22
## [3,] 3 8 13 18 23
## [4,] 4 9 14 19 24
## [5,] 5 10 15 20 25# Calculate the sum and the mean of the elements in the first row and the last row.
## Sum
### First row
sum(transposed_matrix[1,])## [1] 55### Last row
sum(transposed_matrix[n_dims,])## [1] 75## Mean
### First row
mean(transposed_matrix[1,])## [1] 11### Last row
mean(transposed_matrix[n_dims,])## [1] 15# Read about the eigen() function and use it on your matrix.
eigen_lists <- eigen(transposed_matrix, only.values = FALSE, EISPACK = FALSE)
print(eigen_lists)## eigen() decomposition
## $values
## [1] 6.864208e+01+0.000000e+00i -3.642081e+00+0.000000e+00i
## [3] 4.257350e-15+0.000000e+00i -1.270981e-16+4.588876e-16i
## [5] -1.270981e-16-4.588876e-16i
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] 0.3800509+0i -0.76703416+0i 0.54621260+0i 0.1175132+0.0459634i
## [2,] 0.4124552+0i -0.48590617+0i -0.27228461+0i 0.4017692+0.0065072i
## [3,] 0.4448594+0i -0.20477817+0i -0.66418830+0i -0.7435988+0.0000000i
## [4,] 0.4772637+0i 0.07634982+0i -0.03961996+0i -0.1881630-0.2033750i
## [5,] 0.5096680+0i 0.35747782+0i 0.42988027+0i 0.4124793+0.1509044i
## [,5]
## [1,] 0.1175132-0.0459634i
## [2,] 0.4017692-0.0065072i
## [3,] -0.7435988+0.0000000i
## [4,] -0.1881630+0.2033750i
## [5,] 0.4124793-0.1509044i# Look carefully at the elements of $values and $vectors. What kind of numbers are these?
## complex numbers
# Dig in with the typeof() function to figure out their type.
typeof(eigen_lists $ values)## [1] "complex"typeof(eigen_lists $ vectors)## [1] "complex"# If have set your code up properly, you should be able to re-run it and create a matrix of different size because n_dims will change.
## Yep!# Create a list with the following named elements:
# my_matrix, which is a 4 x 4 matrix filled with random uniform values
# my_logical which is a 100-element vector of TRUE or FALSE values. Do this efficiently by setting up a vector of random values and then applying an inequality to it.
# my_letters, which is a 26-element vector of all the lower-case letters in random order.
my_matrix <- matrix(runif(16), nrow = 4, byrow = TRUE)
print(my_matrix)## [,1] [,2] [,3] [,4]
## [1,] 0.4054653 0.7375106 0.174965083 0.4534360
## [2,] 0.8456502 0.2812026 0.572756951 0.3106423
## [3,] 0.9558637 0.5536983 0.039618828 0.9878152
## [4,] 0.2598813 0.8529409 0.009607129 0.2044559my_logical <- runif(100) < 0.5
print(my_logical)## [1] TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## [13] TRUE TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE
## [25] TRUE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE
## [37] FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE
## [49] TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE FALSE
## [61] TRUE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE
## [73] TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE
## [85] TRUE FALSE TRUE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE TRUE
## [97] FALSE FALSE TRUE TRUEmy_letters <- sample(letters[seq(1:26)])
print(my_letters)## [1] "l" "n" "j" "w" "r" "m" "c" "x" "e" "s" "y" "u" "g" "d" "i" "t" "o" "v" "a"
## [20] "f" "k" "q" "b" "z" "h" "p"my_list <- c(my_matrix, my_logical, my_letters)
print(my_list)## [1] "0.405465261312202" "0.845650246134028" "0.955863736337051"
## [4] "0.259881342528388" "0.737510577309877" "0.281202607322484"
## [7] "0.553698347182944" "0.852940906537697" "0.174965082900599"
## [10] "0.572756950976327" "0.0396188276354223" "0.00960712903179228"
## [13] "0.453436034033075" "0.310642284341156" "0.987815206171945"
## [16] "0.204455913277343" "TRUE" "FALSE"
## [19] "TRUE" "TRUE" "FALSE"
## [22] "FALSE" "TRUE" "TRUE"
## [25] "FALSE" "FALSE" "TRUE"
## [28] "FALSE" "TRUE" "TRUE"
## [31] "TRUE" "TRUE" "FALSE"
## [34] "FALSE" "TRUE" "FALSE"
## [37] "TRUE" "TRUE" "TRUE"
## [40] "TRUE" "TRUE" "FALSE"
## [43] "FALSE" "FALSE" "TRUE"
## [46] "TRUE" "TRUE" "TRUE"
## [49] "FALSE" "TRUE" "TRUE"
## [52] "TRUE" "FALSE" "TRUE"
## [55] "TRUE" "FALSE" "FALSE"
## [58] "TRUE" "TRUE" "FALSE"
## [61] "TRUE" "FALSE" "FALSE"
## [64] "FALSE" "TRUE" "TRUE"
## [67] "FALSE" "FALSE" "FALSE"
## [70] "FALSE" "TRUE" "TRUE"
## [73] "FALSE" "FALSE" "TRUE"
## [76] "FALSE" "TRUE" "FALSE"
## [79] "FALSE" "TRUE" "TRUE"
## [82] "TRUE" "FALSE" "TRUE"
## [85] "TRUE" "FALSE" "TRUE"
## [88] "FALSE" "TRUE" "TRUE"
## [91] "TRUE" "FALSE" "FALSE"
## [94] "TRUE" "FALSE" "FALSE"
## [97] "TRUE" "TRUE" "TRUE"
## [100] "TRUE" "TRUE" "FALSE"
## [103] "TRUE" "FALSE" "TRUE"
## [106] "FALSE" "TRUE" "FALSE"
## [109] "FALSE" "TRUE" "FALSE"
## [112] "TRUE" "FALSE" "FALSE"
## [115] "TRUE" "TRUE" "l"
## [118] "n" "j" "w"
## [121] "r" "m" "c"
## [124] "x" "e" "s"
## [127] "y" "u" "g"
## [130] "d" "i" "t"
## [133] "o" "v" "a"
## [136] "f" "k" "q"
## [139] "b" "z" "h"
## [142] "p"# Create a new list, which has the element[2,2] from the matrix, the second element of the logical vector, and the second element of the letters vector.
my_new_list <- list(my_matrix[2,2], my_logical[2], my_letters[2])
print(my_new_list)## [[1]]
## [1] 0.2812026
##
## [[2]]
## [1] FALSE
##
## [[3]]
## [1] "n"# Use the typeof() function to confirm the underlying data types of each component in this list
typeof(my_new_list[[1]])## [1] "double"typeof(my_new_list[[2]])## [1] "logical"typeof(my_new_list[[3]])## [1] "character"# Combine the underlying elements from the new list into a single atomic vector with the c() function.
my_new_vector <- c(my_matrix[2,2], my_logical[2], my_letters[2])
print(my_new_vector)## [1] "0.281202607322484" "FALSE" "n"# What is the data type of this vector?
typeof(my_new_vector)## [1] "character"# Create a data frame with two variables (= columns) and 26 cases (= rows).
# call the first variable my_unis and fill it with 26 random uniform values from 0 to 10
# call the second variable my_letters and fill it with 26 capital letters in random order.
my_unis <- runif(26, min = 0, max = 10)
my_letters <- sample(LETTERS[seq(1:26)])
my_data_frame <- data.frame(my_unis, my_letters)
print(my_data_frame)## my_unis my_letters
## 1 1.1727871 F
## 2 9.7666903 C
## 3 6.3208389 Z
## 4 6.9522760 I
## 5 8.7615724 P
## 6 6.4675606 X
## 7 9.9679205 D
## 8 7.2858485 Y
## 9 6.6427360 W
## 10 5.3580503 Q
## 11 9.8159379 H
## 12 7.8776554 M
## 13 0.8709377 A
## 14 8.4918757 E
## 15 0.3298827 R
## 16 4.6599161 U
## 17 0.3112522 B
## 18 3.1477240 T
## 19 1.1016741 O
## 20 4.7288303 K
## 21 0.9973000 N
## 22 7.5666292 V
## 23 5.0968635 J
## 24 0.7133149 L
## 25 8.8798862 S
## 26 9.7930725 G# 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_data_frame[,1] <- replace(x = my_data_frame[,1], list = sample(nrow(my_data_frame),4), values = NA)
# for the first variable, write a single line of R code to identify which rows have the missing values.
which(is.na(my_data_frame))## [1] 3 9 10 18# for the second variable, sort it in alphabetical order
my_data_frame[,2] <- sort(my_data_frame[,2], decreasing = FALSE)
print(my_data_frame)## my_unis my_letters
## 1 1.1727871 A
## 2 9.7666903 B
## 3 NA C
## 4 6.9522760 D
## 5 8.7615724 E
## 6 6.4675606 F
## 7 9.9679205 G
## 8 7.2858485 H
## 9 NA I
## 10 NA J
## 11 9.8159379 K
## 12 7.8776554 L
## 13 0.8709377 M
## 14 8.4918757 N
## 15 0.3298827 O
## 16 4.6599161 P
## 17 0.3112522 Q
## 18 NA R
## 19 1.1016741 S
## 20 4.7288303 T
## 21 0.9973000 U
## 22 7.5666292 V
## 23 5.0968635 W
## 24 0.7133149 X
## 25 8.8798862 Y
## 26 9.7930725 Z#calculate the column mean for the first variable
mean(complete.cases(my_data_frame[,1]))## [1] 0.8461538