 In this video, we're going to solve question one from exam one for math 2270. So we're given two vectors u, which is 1, negative 1, and v, 2, negative 3 in R2. And we're asked to compute the linear combination 2 plus 2u plus 3v. So this calculation, we're going to take two times the 1, negative 1 that was provided. We're going to take three times the vector 2, negative 3 that was provided. And so doing the scalar multiplication times each number in the associated vector by that. So everything in the first one gets times by 2, 2, and negative 2. And then for the second one, it times everything by 3, you're going to get 3 times 2, which is 6, 3 times negative 3, which is negative 9. And then we add these quantities together in the first entry. We're going to get 2 plus 6, which is 8. And in the second component, we're going to get negative 2 minus 9, which is negative 11. And so we search this amongst the multiple choice and we see that the correct answer here would be choice A.