Question

10 POINTS!

Let u = <-4, 1>, v = <-1, 6>. Find -2u + 4v.

A) <4, 22>
B) <4, 7>
C) <12, -26>
D) <10, -14>

Answer 1

A. <4,22>

Explanation:

This question involves the concepts of addition and scalar multiplication of vectors. It is given that the vector u = <-4, 1> and v = <-1, 6>. To find -2u, simply multiply -2 with the elements of u. This will give:

-2u = <-4*-2, 1*-2> = <8, -2>.

Similarly:

4v = <-1*4, 6*4> = <-4, 24>.

Hence,

-2u + 4v = <8, -2> + <-4, 24> = <8-4, -2+24> = <4,22>.

Answer 2

`\vec{u}=[-4;\ 1];\ \vec{v}=[-1;\ 6]\\\\-2\vec{u}+4\vec{v}=-2[-4;\ 1]+4[-1;\ 6]\\\\=[(-2)(-4);\ (-2)(1)]+[(4)(-1);\ (4)(6)]\\\\=[8;\ -2]+[-4;\ 24]=[8+(-4);\ -2+24]=[4+22]\to A)`