# Chapter 2

## Matrices

Is it true that this is a vector?

`matrix(1)`

No,

because matrix(1) is two-dimensional.

Is it true that this is a vector?

```     [,1]
[1,]    1
```

No,

because this is the result of matrix(1) and matrix(1) is two-dimensional.

How many dimensions does m have when m is

`matrix(1,1)`

two

because m is a matrix.

How many dimensions does m have when m is

`matrix(1,2)`

two

because m is a matrix.

How many dimensions does m have when m is

`matrix(1,2,3)`

two

because m is a matrix.

How many rows does m have when m is

`matrix(1,2,3)`

two

because the second argument in m is 2.

How many columns does m have when m is

`matrix(1,2,3)`

three

because the third argument in m is 3.

What is dim(m) when m is

`matrix(1,2,3)`

2 3

because dim() is the same as asking the values of the dimensions of a matrix.

How many values does m have when m is

`matrix(1,2,3)`

six

because two rows times three columns is six.

What is sum(m) where m is

`matrix(1,2,3)`

six

because there are six values in m and each value is equal to one.

What is sum(m) where m is

`matrix(2,2,3)`

twelve

because there are six values in m and each value is equal to two.

What is length(m) where m is

`matrix(2,2,3)`

six

because there are six values in m.

How many columns does m have where m is

`matrix(15,1,15)`

and

`dim(m) <- c(3,5)`

5

because m was altered to have five columns by dim.

How many columns does m have where m is

`matrix(20,4,5)`

and

`dim(m) <- c(2,20)`

5

because the m is 20, but the number of values produced by dim(m) <- c(2,20) is 40.

What is m[1,3] where m is

`matrix(c(1,2,3),3,3)`

1

because matrix(c(1,2,3),3,3) is

```     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    2    2    2
[3,]    3    3    3```

and the value in the first row, third column is 1.

What is m[1,3] where m is

`matrix(c(1,2,3),2,3)`

2

because matrix(c(1,2,3),2,3) is

```     [,1] [,2] [,3]
[1,]    1    3    2
[2,]    2    1    3
```

and the value in the first row, third column is 2.

What is the name of the second column of m when m is

`matrix(c(1,2,3),3,3)`

and

`colnames(m) <- c("April", "May", "June")`

"May"

because "May" is the second value given to colnames.

What is m[1,3] where m is

`matrix(1:6,2,3)`

5

because matrix(1:6,2,3) is

```     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6```

and the value in the first row, third column is 5.

What is m[1,3] where m is

`matrix(1:6,3,3)`

1

because matrix(1:6,3,3) is

```     [,1] [,2] [,3]
[1,]    1    4    1
[2,]    2    5    2
[3,]    3    6    3```

and the value in the first row, third column is 1.

What is m[1,2] where m is

`c(1,2,3,4)`

and

`dim(m) <- c(2,2)`

3

because m is now

```     [,1] [,2]
[1,]    1    3
[2,]    2    4
```

and the value in the first row, second column is 3.

What is class(m[1,2]) where m is

`c(1,2,3,4)`

and

`dim(m) <- c(2,2)`

integer

because the matrix was made out of an integer vector.

What is m[2,2] where m is

`list(1,"2",3,"4")`

and

`dim(m) <- c(2,2)`
```[]
 "4"```

because m is now

```     [,1] [,2]
[1,] 1    3
[2,] "2"  "4" ```

What is class(m[2,2]) where m is

`list(1,"2",3,"4")`

and

`dim(m) <- c(2,2)`

list

because the matrix was made out of a list.