Step by step
The question
Question: work out this difference of two matrices.
[6, 0; −1, 4] − [2, −3; 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 take away matrices of the same size, so every entry has a partner in the same place.
2 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, 0 − (−3); −1 − 5, 4 − 1]
Careful!
Taking away a negative is adding.
0 − (−3) = 0 + 3 = 3.
Careful: not 0 − (−3) = −3 ✗
Now we work out each one.
The answer: rows 4, 3 and −6, 3.
= [4, 3; −6, 3]
3 Check
Let's check by adding back.
The answer plus the second matrix must give back the first one.
4 + 2 = 6, 3 + (−3) = 0
−6 + 5 = −1, 3 + 1 = 4
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; −6, 3]