Step by step
The question
Question: work out this sum of two matrices.
[1, 3, 2] + [4, 0, 5]
A matrix is numbers in rows and columns, inside big brackets.
Each number in a matrix is called an entry.
1 Check the sizes
Both are 1 by 3: the same size.
Good!
We can only add matrices of the same size, so every entry has a partner in the same place.
2 Add the matching entries
We add the numbers in the same place.
Top left: 1 and 4.
So we write 1 + 4 there.
And the same in every place.
= [1 + 4, 3 + 0, 2 + 5]
Careful!
We add only the two entries in the same place: top left with top left, and so on.
Careful: only entries in the same place
Now we work out each one.
The answer: the row 5, 3, 7.
= [5, 3, 7]
3 Check
Let's check by taking away.
The answer minus the second matrix must give back the first one.
5 − 4 = 1, 3 − 0 = 3, 7 − 5 = 2
We get the first matrix back.
So the answer is right!
Let's look back.
First: check the sizes.
Then: add the matching entries.
Last: check.
Answer
= [5, 3, 7]