## Description

The basic Sage command to enter the matrix

(1)is `A = matrix([[1, 2, 3], [4, 5, 6]])`.

## Sage Cell

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6]])
A
```

## Options

#### Option

The matrix $A$ is a $2 \times 3$ matrix with entries in the integers.

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6]])
A.parent()
```

#### Option

The matrix $A$ below has entires in the rationals, `QQ`. We may replace `QQ` with `RR` (the floating point real numbers) or `CC` (the floating point complex numbers).

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6]])
A.parent()
```

#### Option

The number of rows (2) and columns (3) can be entered.

#### Code

```
A = matrix(QQ, 2, 3, [[1, 2, 3], [4, 5, 6]])
A
```

#### Option

You can specify how many rows the matrix will have and provide one big grand list of entries, which will get chopped up, row by row, if you prefer.

#### Code

```
A = matrix(QQ, 2, [1, 2, 3, 4, 5, 6])
A
```

#### Option

The commands `A.nrows()` and `A.ncols()` will return the number of rows and columns of the matrix $A$, respectively.

#### Code

```
A = matrix(QQ, 2, 3, [[1,2,3],[4,5,6]])
A.nrows(), A.ncols()
```

#### Option

The command `A.base_ring()` will return the ring or field for the entries in the matrix $A$.

#### Code

```
A = matrix(RR, [[1, 2, 3], [4, 5, 6]])
A.base_ring()
```

#### Option

Rows in the matrix $A$ and numbered 0 to 1, while columns are numbered 0 to 2. The command `A[i,j]` returns the entry in the $i$th row and $j$th column of the matrix $A$ or 6.

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6]])
A[1,2]
```

## Tags

CC: math.la.i.mat

Primary Tags: linear algebra

Secondary Tags: matrices

## Related Cells

None

## Attribute

Permalink: http://linear.ups.edu/html/section-RREF.html

Author: R. Beezer

Date: 24 Jul 2017 13:53

Submitted by: Tom Judson