Matrix Singularity

## Description

We can use the `.is_singular()` command to see if a matrix, say

\begin{align} A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}, \end{align}

is invertible or not. If the command returns false, the matrix is invertible, and if it returns true, then the matrix is not invertible, or singular.

## Sage Cell

#### Code

```
A = matrix(QQ, [[1, 2, 3], [4, 5, 6], [7, 8, 9]])
A.is_singular()
```

## Options

None.

## Tags

CC:

Primary Tags: Linear algebra: Matrices.

Secondary Tags: Matrices: Matrix basics, Matrix inverses.

## Related Cells

- Matrices in Sage. Matrices in Sage.
- Elementary Row Operations on Matrices Using Sage to perform elementary row operations.
- Augmented Matrices. Augmenting a matrix with a column vector.
- The determinant of a matrix. Taking the determinant of a matrix.
- The rank of a matrix. Calculating the rank of a matrix.
- The RREF of a matrix. Computing the RREF of a matrix.
- Finding the Pivot Columns of a Matrix. Finding the pivot columns of a matrix.
- Finding the Free Columns of a Matrix. Finding the free columns of a matrix.
- The inverse of a matrix. Computing the inverse of a matrix.
- Constructing Identity Matrices. A special command to create an identity matrix.

## Attribute

Permalink:

Author: R. Beezer

Date: 01 Mar 2020 21:04

Submitted by: Zane Corbiere