Question Video: Scalar Multiplication of a Vector Mathematics

Video Transcript

Given that 𝐀 is the vector six, 11, find a half 𝐀.

In this question, we have a vector 𝐀. And this vector is given component-wise. We’re asked to find the value of one-half times 𝐀. So we’re asked to find the product between a constant and a vector. We can do this by using scalar multiplication. To do this, we need to recall for constant 𝑘 and vector 𝐚, 𝐛, 𝑘 times the vector 𝐚, 𝐛 is equal to the vector 𝑘𝐚, 𝑘𝐛. In other words, we multiply each of the components of our vector by our value of 𝑘.

So to evaluate one-half multiplied by 𝐀, we want to multiply each of the components of 𝐀 by one-half. This gives us the vector one-half times six, one-half times 11. And we can evaluate each of these components separately. One-half times six is equal to three, and one-half times 11 is equal to 5.5. This gives us our final answer of the vector three, 5.5.

Therefore, we were able to show if 𝐀 is the vector six, 11, then we can evaluate one-half multiplied by 𝐀 by multiplying each component by one-half. We got one-half 𝐀 is equal to the vector three, 5.5.