Given that 𝐀 is the vector negative three, two, find negative four times 𝐀.
In this question, we’re given a vector 𝐀, and this vector is given component-wise. We need to determine the value of negative four multiplied by 𝐀. To answer this question, we first need to notice we’re asked to multiply a constant by a vector. And we can do this by using scalar multiplication between a constant and a vector. We recall we just need to multiply every component of our vector by our scalar. In other words, 𝑘 times the vector 𝑥𝑦 is equal to the vector 𝑘𝑥, 𝑘𝑦.
So to multiply our vector by negative four, we need to multiply each of the components of our vector 𝐀 by negative four. This gives us the vector negative four times negative three, negative four times two, and we can just calculate each of these components. We get the vector 12, negative eight, which is our final answer.
Therefore, by using the fact to multiply a vector by a scalar, we just multiply each of the components of our vector by our scalar, we were able to show if 𝐀 is the vector negative three, two, then negative four times 𝐀 is the vector 12, negative eight.