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

Step by step

The question

Question: work out this.

2[1, 3; −1, 0] + [4, −2; 5, 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 add 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.

2 in front means: every entry times 2.

We write 2 × in front of each one.

= [2 × 1, 2 × 3; 2 × (−1), 2 × 0] + [4, −2; 5, 1]

Now we work out each one.

2 times 1 is 2, and so on.

= [2, 6; −2, 0] + [4, −2; 5, 1]

3 Add the matching entries

We add the numbers in the same place.

Top left: 2 and 4.

So we write 2 + 4 there.

And the same in every place.

= [2 + 4, 6 + (−2); −2 + 5, 0 + 1]

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 6, 4 and 3, 1.

= [6, 4; 3, 1]

4 Check

Let's check by taking away.

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

6 − 4 = 2, 4 − (−2) = 6

3 − 5 = −2, 1 − 1 = 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: add the matching entries.

Last: check.

Answer