Step by step
The question
Question: work out 3 times this matrix.
3[2, 1; 0, 4]
A matrix is numbers in rows and columns, inside big brackets.
Each number in a matrix is called an entry.
1 Times every entry
3 in front means: every entry times 3.
We write 3 × in front of each one.
= [3 × 2, 3 × 1; 3 × 0, 3 × 4]
Careful!
Every entry gets times 3, in every row.
Not only the first one.
Careful: every entry × 3, every row
Now we work out each one.
3 times 2 is 6, and so on.
The answer: rows 6, 3 and 0, 12.
= [6, 3; 0, 12]
2 Check
Let's check by dividing back: each entry divided by 3.
6 ÷ 3 = 2, 3 ÷ 3 = 1
0 ÷ 3 = 0, 12 ÷ 3 = 4
We get the first matrix back.
So the answer is right!
Let's look back.
First: times every entry.
Last: check.
Answer
= [6, 3; 0, 12]