Calculate [-2, 5; 3, -1] + [4, -3; -6, 2] Step by Step

Step by step

Question: work out this sum of two matrices.

[−2, 5; 3, −1] + [4, −3; −6, 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, 5 + (−3); 3 + (−6), −1 + 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 2, 2 and −3, 1.

= [2, 2; −3, 1]

Let's check by taking away.

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

2 − 4 = −2, 2 − (−3) = 5

−3 − (−6) = 3, 1 − 2 = −1

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

= [2, 2; −3, 1]