Calculate [5, -2, 1; 0, 3, -4] + [-1, 2, 6; 3, -3, 2] Step by Step

Step by step

Question: work out this sum of two matrices.

[5, −2, 1; 0, 3, −4] + [−1, 2, 6; 3, −3, 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 3: 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: 5 and −1.

So we write 5 + (−1) there.

And the same in every place.

= [5 + (−1), −2 + 2, 1 + 6; 0 + 3, 3 + (−3), −4 + 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 4, 0, 7 and 3, 0, −2.

= [4, 0, 7; 3, 0, −2]

Let's check by taking away.

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

4 − (−1) = 5, 0 − 2 = −2, 7 − 6 = 1

3 − 3 = 0, 0 − (−3) = 3, −2 − 2 = −4

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

= [4, 0, 7; 3, 0, −2]