A good answer might be:

  w         =   (-5, 5)T         v   =   (5, 1)T
kv   =   (-4.2, -.85)T       u   =   (-1.3, 5.8)T

Eyeball Estimate

Those answers were done by reading off the picture. No guarantee that they are accurate. So let us check:

First: Does w  =  kv + u?

(-4.2, -0.85)T + (-1.3, 5.8)T  =  (-5.5, 4.95)T  =  w   (almost)

Next: Does v · u  =  0.0 ?

(5, 1)T · (-1.3, 5.8)T  =  -6.5 + 5.8  =  -0.7  =  0.0   (almost)


QUESTION 13:

Can the projection of w onto v point in the opposite direction of v ?