We often wish to examine part of a set of data. Suppose that our data is stored in the matrix A.

> A = matrix(1:16, 4, 4)
> A
    [,1] [,2] [,3] [,4]
[1,]   1    5    9    13
[2,]   2    6    10   14
[3,]   3    7    11   15
[4,]   4    8    12   16

Then, typing

> A[2, 3]
[1] 10

will select the element corresponding to the second row and the third column. The first number after the open-bracket symbol [ always refers to the row, and the second number always refers to the column. We can also select multiple rows and columns at a time, by providing vectors as the indices.

Note: In R indexing starts at 1, meaning the first element of a vector, matrix or any kind of data structure is at index 1. Most of the other languages such as Python or Java start indexing at 0

> A[c(1, 3), c(2, 4)]
    [,1] [,2]
[1,]   5   13
[2,]   7   15

> A[1:3, 2:4]
    [,1] [,2] [,3]
[1,]    5   9   13
[2,]    6   10  14
[3,]    7   11  15

> A[1:2,]
    [,1] [,2] [,3] [,4]
[1,]    1   5   9   13
[2,]    2   6   10  14

> A[, 1:2]
    [,1] [,2]
[1,]    1   5
[2,]    2   6
[3,]    3   7
[4,]    4   8

The last two examples include either no index for the columns or no index for the rows. These indicate that R should include all columns or all rows, respectively. R treats a single row or column of a matrix as a vector.

> A[1,]
[1] 1 5 9 13

The use of a negative sign - in the index tells R to keep all rows or columns except those indicated in the index.

> A[-c(1, 3),]
[,1] [,2] [,3] [,4]
[1,] 2 6 10 14
[2,] 4 8 12 16
> A[-c(1, 3), -c(1, 3, 4)]
[1] 6 8

Questions

• Select the first three rows and columns from the matrix A and store it in A1
• From the the first and third row, select the elements that are in the second and fourth column and store it in A2
• Select the element on the second row and the fourth column and store it in A3
• Select the fourth column and store it in A4
• Add the first and second row together with the + operator and store it in A5

Use the code below as a starting point.