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

a) draw these vectors in ℝ2 .

b) find scalars λ1 and λ2 such that w = λ1u + λ2v.

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)

We have to find the values of a and b

]

Equate the corresponding terms

Divide II equation by 2 to get

Eliminate a

-5 = 5b: b=-1

a=-2

Hence

w = 2u-v