Step by step
The question
Question: work out −2 times this matrix.
−2[3, −1; 0, 5]
A matrix is numbers in rows and columns, inside big brackets.
Each number in a matrix is called an entry.
1 Times every entry
−2 in front means: every entry times −2.
We write −2 × in front of each one.
= [−2 × 3, −2 × (−1); −2 × 0, −2 × 5]
Careful!
Every entry gets times −2, in every row.
Not only the first one.
Careful: every entry × −2, every row
Now we work out each one.
−2 times 3 is −6, and so on.
The answer: rows −6, 2 and 0, −10.
= [−6, 2; 0, −10]
2 Check
Let's check by dividing back: each entry divided by −2.
−6 ÷ (−2) = 3, 2 ÷ (−2) = −1
0 ÷ (−2) = 0, −10 ÷ (−2) = 5
We get the first matrix back.
So the answer is right!
Let's look back.
First: times every entry.
Last: check.
Answer
= [−6, 2; 0, −10]