Step by step
The question
Question: find −2u, when u = ⟨2, 0, −1⟩.
u = ⟨2, 0, −1⟩
1 Multiply by the numbers
−2u means −2 times every part of u.
−2u = ⟨−2 × 2, −2 × 0, −2 × (−1)⟩
−2 times 2 is −4.
−2 times 0 is 0.
−2 times (−1) is 2.
−2u = ⟨−4, 0, 2⟩
So −2u = ⟨−4, 0, 2⟩.
−2u = ⟨−4, 0, 2⟩
Careful!
The number multiplies every part, not only the first one.
Careful: not ⟨−4, 0, −1⟩ ✗
2 Check
Let's check with a picture.
Here is u.
−2u points the opposite way, because of the minus.
Divide each part of the answer by −2.
We get back ⟨2, 0, −1⟩.
Right!
⟨−4, 0, 2⟩ ÷ (-2) = ⟨2, 0, −1⟩
Let's look back.
First: multiply by the numbers.
Last: check.
Answer
Careful: not ⟨−4, 0, −1⟩ ✗