# Vector Addition in MATLAB and Octave

To add vectors in MATLAB and Octave, utilize the `+` operator.

Given vectors `v` and `w`:

**v + w**

## Example

**Example 1**

Define vector `v`:

>> v=[1;2;3]

Define another vector `w`:

>> w=[4;5;6]

Both `v` and `w` are column vectors consisting of three elements.

To compute their sum, simply use v + w

>> v+w

ans =

5

7

9

The resulting vector is the sum of `v` and `w`.

**Example 2**

Define a row vector `z`:

>> z=[1 2]

z = 1 2

Define a column vector `u`:

>> u=[3;4]

u =

3

4

To add vectors `z` and `u`, execute:

>> z+u

The output is:

ans =

4 5

5 6

**Note**. In this instance, the result is a matrix. This is because the addition involves a row vector and a column vector. Mathematically, the operation is represented as: $$ z+u = \begin{pmatrix} 1 & 2 \end{pmatrix} + \begin{pmatrix} 3 \\ 4 \end{pmatrix} = \begin{pmatrix} 1+3 & 2+3 \\ 1+4 & 2+4 \end{pmatrix} = \begin{pmatrix} 4 & 5 \\ 5 & 6 \end{pmatrix} $$

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