Given that 𝚨 is the vector two, five, find three 𝚨.
In this question, we’re given a vector 𝚨 component-wise, and we’re asked to find the value of three times 𝚨. Since three is a constant and 𝚨 is a vector, this is this multiplication between a scalar and a vector. So we’re going to need to do this by using scalar multiplication. To do this, let’s start by recalling how we multiply a constant and a vector. We recall to multiply any constant 𝑘 by a vector 𝐚, 𝐛, we do this component-wise. In other words, 𝑘 times the vector 𝐚, 𝐛 is equal to the vector 𝑘𝐚, 𝑘𝐛.
We want to use this to find three times the vector 𝚨. So we’re going to need to multiply all of the components of our vector 𝚨 by three. This gives us the vector three times two, three times five. And of course, we can calculate each of the expressions in our components. Three times two is equal to six and three times five is equal to 15. This gives us our final answer of the vector six, 15. Therefore, given the vector 𝚨 is the vector two, five, we were able to find three times 𝚨 by multiplying each of the components of 𝚨 by three. We got that three 𝚨 is equal to the vector six, 15.