Question

Let u = (1,2), v = (−3,4), and w = (5,0)

Answer 1

Answer:

w-2u-v

Step-by-step explanation:

Given are three vectors u, v and w.

In R^2 we treat first element as x coordinate and 2nd element as y coordinate.

Thus we mark (1,2) in the I quadrant, (-3,4) in II quadrant and (5,0) on positive x axis 5 units form the origin.

b) $w=au+bv$

We have to find the values of a and b

$(5,0) = a(1,2)+b(-3,4)$]

Equate the corresponding terms

$5=a-3b\\0=2a+4b$

Divide II equation by 2 to get

$0=a+2b$

Eliminate a

-5 = 5b: b=-1

a=-2

Hence

w = 2u-v