# Documentation

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# `linalg`::`delCol`

Delete matrix columns

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## Syntax

```linalg::delCol(`A`, `c`)
linalg::delCol(`A`, `c1 .. c2`)
linalg::delCol(`A`, `list`)
```

## Description

`linalg::delCol(A, c)` returns a copy of the matrix A in which the column with index c is deleted.

`linalg::delCol(A, c1.. c2)` deletes those columns whose indices are in the range ```c1.. c2```. If ```c2< c1``` then the input matrix `A` is returned.

`linalg::delCol(A, list)` deletes those columns whose indices are contained in `list`.

If all columns are deleted then `NIL` is returned.

## Examples

### Example 1

We define the following matrix:

`A := matrix([[1, 2, 3, 4], [5, 6, 7, 8]])`

and demonstrate the three different input formats for `linalg::delCol`:

`linalg::delCol(A, 2)`

`linalg::delCol(A, [1, 3])`

`linalg::delCol(A, 2..4)`

### Example 2

We compute the inverse of the 2×2 matrix:

```MatQ := Dom::Matrix(Dom::Rational): A := MatQ([[3, 2], [5, -4]])```

by appending the 2×2 identity matrix to the right side of A and applying the Gauss-Jordan algorithm provided by the function `linalg::gaussJordan`:

`B := linalg::gaussJordan(A . MatQ::identity(2))`

We get the inverse of `A` by deleting the first two columns of the matrix `B`:

`AI := linalg::delCol(B, 1..2)`

Finally, we check the result:

`A * AI, AI * A`

Note: The inverse of `A` can be computed directly by entering `1/A`.

## Parameters

 `A` An m×n matrix of a domain of category `Cat::Matrix` `c` The column index: a positive integer less or equal to n `c1 .. c2` A range of column indices (positive integers less or equal to n) `list` A list of column indices (positive integers less or equal to n)

## Return Values

Matrix of a domain of category `Cat::Matrix(R)`, where `R` is the component ring of `A`, or `NIL`.