Calculate [7, 4; 6, 9] - [3, 1; 2, 5] Step by Step

Step by step

Question: work out this difference of two matrices.

[7, 4; 6, 9] − [3, 1; 2, 5]

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 take away matrices of the same size, so every entry has a partner in the same place.

We take away the numbers in the same place.

Top left: 7 and 3.

So we write 7 − 3 there.

And the same in every place.

= [7 − 3, 4 − 1; 6 − 2, 9 − 5]

Careful!

The order matters.

Always the first matrix minus the second, in every place.

Careful: first matrix − second matrix

Now we work out each one.

The answer: rows 4, 3 and 4, 4.

= [4, 3; 4, 4]

Let's check by adding back.

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

4 + 3 = 7, 3 + 1 = 4

4 + 2 = 6, 4 + 5 = 9

We get the first matrix back.

So the answer is right!

Let's look back.

First: check the sizes.

Then: take away the matching entries.

Last: check.

Answer

= [4, 3; 4, 4]