# Tutorial Video

# Element by Element Multiplication

Element by element multiplication (the dot product) `.*`

works differently from Array multiplication `*`

be careful not to confuse the two.

**Multiplication of Scalars**

Assuming one buys 5 pens and the price of a pen is £2. Then the amount of cash spent on pens is £10

`5 pens .* £2 = 5*£2 = £10`

To write this in MATLAB we would use

`5.*2`

Note for a 1 by 1 scalar array multiplication and element by element multiplication are identical.

**(Dot Product) of Column Vectors**

If we ordered 5 pens which cost £2 each and 3 pads which cost £6 each then

i.e. we would spend a total of £10 on pens and £18 on pads.

To write this in MATLAB we would use

`[5;3].*[2;6]`

**(Dot Product) of Matrices**

If the man in the red house bought 5 pens and 3 pads and the women in the green house bought 7 pens and 5 pads from the same shop costing £2 a pen and £6 a pad then:

i.e. the man spent £10 on pens and £18 on pads and the woman spent £14 on pens and £30 on pads.

To write this in MATLAB we would use

`[5,7;3,5].*[2,2;6,6]`

Alternatively if the woman living in the green house went to a more expensive shop where the price of pens and pads was £3 and £7 respectively

i.e. the man would once again spend £10 on pens and £18 on pads and this time the woman would spend £21 on pens and £35 on pads.

To write this in MATLAB we would use

`[5,7;3,5].*[2,3;6,7]`