Calculate [2, 1; 0, 3] + [4, 5; 1, 2] Step by Step

Step by step

Question: work out this sum of two matrices.

[2, 1; 0, 3] + [4, 5; 1, 2]

A matrix is numbers in rows and columns, inside big brackets.

Each number in a matrix is called an entry.

Both are 2 by 2: the same size.

Good!

We can only add matrices of the same size, so every entry has a partner in the same place.

We add the numbers in the same place.

Top left: 2 and 4.

So we write 2 + 4 there.

And the same in every place.

= [2 + 4, 1 + 5; 0 + 1, 3 + 2]

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: rows 6, 6 and 1, 5.

= [6, 6; 1, 5]

Let's check by taking away.

The answer minus the second matrix must give back the first one.

6 − 4 = 2, 6 − 5 = 1

1 − 1 = 0, 5 − 2 = 3

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

= [6, 6; 1, 5]