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

Step by step

The question

Question: work out this.

[4, 2; 1, 3] − 3[1, 0; 2, −1]

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

Each number in a matrix is called an entry.

1 Check the sizes

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.

2 Times first

Like the order of operations: times comes before plus and minus.

3 in front means: every entry of the second matrix times 3.

= [4, 2; 1, 3] − [3 × 1, 3 × 0; 3 × 2, 3 × (−1)]

Now we work out each one.

= [4, 2; 1, 3] − [3, 0; 6, −3]

3 Take away the matching entries

We take away the numbers in the same place.

Top left: 4 and 3.

So we write 4 − 3 there.

And the same in every place.

= [4 − 3, 2 − 0; 1 − 6, 3 − (−3)]

Careful!

Taking away a negative is adding.

3 − (−3) = 3 + 3 = 6.

Careful: not 3 − (−3) = 0 ✗

Now we work out each one.

The answer: rows 1, 2 and −5, 6.

= [1, 2; −5, 6]

4 Check

Let's check by adding back.

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

1 + 3 = 4, 2 + 0 = 2

−5 + 6 = 1, 6 + (−3) = 3

We get the first matrix back, after the times.

So the answer is right!

Let's look back.

First: check the sizes.

Then: times first.

Then: take away the matching entries.

Last: check.

Answer