## `linalg::setCol` -- change a column of a matrix

#### Introduction

`linalg::setCol``(A, p, c)` returns a copy of matrix A with the p-th column replaced by the column vector c.

#### Call(s)

`linalg::setCol(A, p, c)`

#### Parameters

`A` | - | an m x n matrix of a domain of category `Cat::Matrix`
`c` | - | a column vector, or a list that can be converted into a column vector of the domain `Dom::Matrix(R)`, where `R` is the component ring of `A` (a column vector is an m x 1 matrix)

#### Returns

a matrix of the same domain type as `A`.

#### Related Functions

`linalg::col`, `linalg::delCol`, `linalg::delRow`, `linalg::row`, `linalg::setRow`

#### Details

- If `c` is a list with at most m elements, then `c` is converted into a column vector. An error message is returned if the conversion is not possible (e.g., if an element of the list cannot be converted into an object of the component ring of `A`; see example 2).

#### Example 1

We define a matrix over the rationals:

    >> MatQ := Dom::Matrix(Dom::Rational):
       A := MatQ([[1, 2], [3, 2]])

                                    +-      -+
                                    |  1, 2  |
                                    |        |
                                    |  3, 2  |
                                    +-      -+

and replace the 2nd column by the 2x1 zero vector:

    >> linalg::setCol(A, 2, MatQ([0, 0]))

                                    +-      -+
                                    |  1, 0  |
                                    |        |
                                    |  3, 0  |
                                    +-      -+

#### Example 2

We create the 2x2 zero matrix over Z6:

    >> B := Dom::Matrix(Dom::IntegerMod(6))(2, 2)

                              +-                  -+
                              |  0 mod 6, 0 mod 6  |
                              |                    |
                              |  0 mod 6, 0 mod 6  |
                              +-                  -+

and replace the 2nd column by the vector [[1,-1]]. We give the column vector in form of a list. Its elements are converted implicitly into objects of the component ring of `B`:

    >> linalg::setCol(B, 2, [1, -1])

                              +-                  -+
                              |  0 mod 6, 1 mod 6  |
                              |                    |
                              |  0 mod 6, 5 mod 6  |
                              +-                  -+

The following input leads to an error message because the number `1/3` can not be converted into an object of type `Dom::IntegerMod(6)`:

    >> linalg::setCol(B, 1, [1/3, 0])

          Error: invalid column vector [linalg::setCol]

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