Step by step
The question
Question: multiply these two matrices.
[3, 1; −2, 5] × [−1; 4]
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 × (−1) + 1 × 4; −2 × (−1) + 5 × 4]
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.
= [−3 + 4; 2 + 20]
Then we add.
The answer: the column 1, 22.
= [1; 22]
4 Check
Let's check each entry, adding its products the other way round.
4 + (−3) = 1
20 + 2 = 22
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
= [1; 22]