Problem 1: (50 points)

  1. Create a 4 by 5 matrix of the numbers 1:20 called M by specifying the nrow and byrow = TRUE arguments in the matrix fucntion.
M <- matrix(1:20, nrow = 4, byrow = TRUE)
M
##      [,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
  1. Using indexing notation, grab first two rows of M
M[1:2, ]
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    2    3    4    5
## [2,]    6    7    8    9   10
  1. using indexing notation, grab first and third columns of M
M[, c(1, 3)]
##      [,1] [,2]
## [1,]    1    3
## [2,]    6    8
## [3,]   11   13
## [4,]   16   18
  1. Create vector V = c(21, 22, 23, 24, 25)
V <- c(21, 22, 23, 24, 25)
V
## [1] 21 22 23 24 25
  1. Use rbind function to create a matrix B using the matrix M and the vector V
B <- rbind(M, V)
  1. Confirm that B is a matrix
is.matrix(B)
## [1] TRUE

Problem 2: (50 points)

  1. Create a 3 by 5 matrix of the numbers 11:25 calledNby specifying thenrowandbyrow = FALSEarguments in thematrix` function.
N <- matrix(11:25, nrow = 3, byrow = FALSE)
N
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   11   14   17   20   23
## [2,]   12   15   18   21   24
## [3,]   13   16   19   22   25
  1. Write a R code to extract the sub_matrix of N whose 4th column values are grater than 20
subN <- N[N[, 4] > 20, , drop = FALSE]
subN
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   12   15   18   21   24
## [2,]   13   16   19   22   25