Step by step
The question
Question: multiply these two matrices.
[3, −1] × [2, 4; 1, 5]
1 Check the sizes
2 Row times column
Each entry of the answer is one row of the first matrix, times one column of the second.
= [3 × 2 + −1 × 1, 3 × 4 + −1 × 5]
Careful!
Always a row of the first matrix with a column of the second.
Never the other way.
Careful: row of the first × column of the second
3 Work out each entry
First we work out every times.
= [6 + (−1), 12 + (−5)]
Then we add.
The answer: the row 5, 7.
= [5, 7]
4 Check
Let's check each entry, adding its products the other way round.
−1 + 6 = 5, −5 + 12 = 7
Every entry matches.
So the answer is right!
Let's look back.
First: check the sizes.
Then: row times column.
Then: work out each entry.
Last: check.
Answer
= [5, 7]