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

Step by step

The question

Question: work out this.

3[2, −1; 4, 0] − 2[1, 2; −3, 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.

Every entry of the first matrix times 3, every entry of the second times 2.

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

Now we work out each one.

= [6, −3; 12, 0] − [2, 4; −6, 2]

3 Take away the matching entries

We take away the numbers in the same place.

Top left: 6 and 2.

So we write 6 − 2 there.

And the same in every place.

= [6 − 2, −3 − 4; 12 − (−6), 0 − 2]

Careful!

Taking away a negative is adding.

12 − (−6) = 12 + 6 = 18.

Careful: not 12 − (−6) = 6 ✗

Now we work out each one.

The answer: rows 4, −7 and 18, −2.

= [4, −7; 18, −2]

4 Check

Let's check by adding back.

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

4 + 2 = 6, −7 + 4 = −3

18 + (−6) = 12, −2 + 2 = 0

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