Find 4u+2v, if u=⟨−3,−8⟩ and v=⟨7,−2⟩.

Question

This is a question I have in math and I have no clue how to do it.

Answer 1

u and v are vectors such that u = -3i - 8j and v = 7i - 2j.

Scalar multiplication of a vector is simply A(xi + yj) = Axi + Ayj for a scalar A.

Vector addition is simply component addition such that (ai + bj) + (ci + dj) = (a + c)i + (b + d)j.

Thus,

4u + 2v = 4(-3i - 8j) + 2(7i - 2j) = -12i -32j +14i -4j = 2i - 36j = <2, -36>