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

Step by step

Question: work out this difference of two matrices.

[1, 2; 3, 4; 5, 6] − [6, 5; 4, 3; 2, 1]

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

Each number in a matrix is called an entry.

Both are 3 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: 1 and 6.

So we write 1 − 6 there.

And the same in every place.

= [1 − 6, 2 − 5; 3 − 4, 4 − 3; 5 − 2, 6 − 1]

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 −5, −3, −1, 1 and 3, 5.

= [−5, −3; −1, 1; 3, 5]

Let's check by adding back.

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

−5 + 6 = 1, −3 + 5 = 2

−1 + 4 = 3, 1 + 3 = 4

3 + 2 = 5, 5 + 1 = 6

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

= [−5, −3; −1, 1; 3, 5]