# Tutorial Video

**Addition of Scalars**

Lets first look at the addition of scalars i.e. 1 by 1 matrices. Let's now for the sake of conceptualisation prescribe the values we have to objects. If we have 3 pens at home and order 5 more pens then when our order arrives we will have:

`3 pens + 5 pens = 8 pens`

To write this in MATLAB we would use

`3+5`

**Addition of Column Vectors**

Now let us conceptualise a more complicated example. Assume we have 3 pens and 2 pads at home, we then make a order for 5 more pens and 3 more pads.

Since pens and pads are separate objects we classify them as such. Let's essentially treat each item as a scalar:

`3 pens + 5 pens = 8 pens`

`2 pads + 3 pads = 5 pads`

If these are instead written as a column vector we will have:

To write this in MATLAB we would use

`[3;2]+[5;3]`

If I instead had 2 pens on my desk and I ordered 3 pads then in column vector notation I would have:

With this notation bare in mind that pens and pads are separate objects meaning a pen cannot transform into a pad and a pad cannot transform into a pen!

To write this in MATLAB we would use

`[2;0]+[0;3]`

**Note how we have to use zeros here to denote that we don't have a pad or pen in the first and second column vectors respectively. Element by Element operations will only work if the Arrays have the same amount of Elements. **

**Addition of a Matrices**

Okay so far, so good. Let's make things slightly more complicated now. Assume there are two neighbours, neighbour 1 lives in the red house and he has 3 pens and 2 pads, he makes an order for 5 pens and 3 pads and neighbour 2 lives in the green house and she has 2 pens and 2 pads, she makes an order for 7 pens and 5 pads. In this case after the order the man in the red house would have 8 pens and 5 pads whilst the woman would have 9 pens and 7 pads.

To write this in MATLAB we would use

`[3,2;2,2]+[5,7;3,5]`

Now obviously we can conceive of more complicated scenarios where there are say 5 neighbours and they each have and order 7 different item types of stationary which would give a 7 by 5 matrix opposed to the 2 by 2 case above.