SWC MCQ + lesson
Consider the following matrix, m:
m <- matrix(1:12, nrow = 4, byrow = TRUE)
m
## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 4 5 6
## [3,] 7 8 9
## [4,] 10 11 12
Which solution prints the answer 3?
A. min(m[2, ])
B. mean(c(m[1, ], m[2, 3]))
C. max(m[, 3])
D. m[2, 3] + dim(m)[2]
First let's review creating and manipulating arrays, and a few built-in functions (c, sum, min, max, mean, length)
x = c(10, 20, 30, 40)
x
## [1] 10 20 30 40
R indexes arrays from 1, as opposed to zero, as in some other languages like Perl or Python. Let's access the second element of x:
x[2]
## [1] 20
Let's now create a subset of x that contains only the second and third elements of x:
xs = x[2:3]
xs
## [1] 20 30
Now, let's create a matrix (or, you can think of this as a two-dimensional vector). Remember, you can get help about this function with ?matrix.
mat = matrix(1:20, nrow = 5)
mat
## [,1] [,2] [,3] [,4]
## [1,] 1 6 11 16
## [2,] 2 7 12 17
## [3,] 3 8 13 18
## [4,] 4 9 14 19
## [5,] 5 10 15 20
By default R fills in the matrix by columns. Set byrow=TRUE to fill in by rows:
mat = matrix(1:20, nrow = 5, byrow = TRUE)
mat
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 5 6 7 8
## [3,] 9 10 11 12
## [4,] 13 14 15 16
## [5,] 17 18 19 20
We can access elements of the matrix just like accessing elements of an array, but this time using a comma to separate the row and column indices. For example, M[r,c] will return the element(s) in the rth row and cth column of matrix M. Let's try it.
mat[2, 4]
## [1] 8
Above we asked for a single element of the array. We can also get a smaller two-dimensional matrix by specifying which rows and columns we want. Also, we can get an entire row by leaving off the column index, or we can get the entire column by leaving off the row index:
mat
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 5 6 7 8
## [3,] 9 10 11 12
## [4,] 13 14 15 16
## [5,] 17 18 19 20
mat[4:5, 1:3]
## [,1] [,2] [,3]
## [1,] 13 14 15
## [2,] 17 18 19
mat[5, ] #fifth row
## [1] 17 18 19 20
mat[, 2] # second column
## [1] 2 6 10 14 18
Finally, a useful function for examining and manipulating matrices is the dim() function. For a two-dimensional matrix, it returns a two element array, with the first element being the number of rows, and second element being the number of columns. You can access the row and column numbers by slicing what dim() returns.
mat
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 5 6 7 8
## [3,] 9 10 11 12
## [4,] 13 14 15 16
## [5,] 17 18 19 20
dim(mat)
## [1] 5 4
dim(mat)[1] # number of rows
## [1] 5
dim(mat)[2] # number of columns
## [1] 4
mat[dim(mat)[1], dim(mat)[2]] # same as mat[5,4]
## [1] 20
mat[5, 4]
## [1] 20
Consider the following matrix m2.
m2 = matrix(1:30, nrow = 5)
m2
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 6 11 16 21 26
## [2,] 2 7 12 17 22 27
## [3,] 3 8 13 18 23 28
## [4,] 4 9 14 19 24 29
## [5,] 5 10 15 20 25 30
Which of the following assignments will produce a vector, a, where a[2] returns 14?
A. a = m2[1, 2:3]
B. a = min(m2[, 1])
C. a = m2[3:5, 3]
D. a = m2[4, 3:5]