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Answer:

  w         =   (-5, 5)T         v   =   (5, 1)T
kv   =   (-3.8, -.8)T       u   =   (-1.3, 5.6)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?

(-3.8, -0.8)T + (-1.3, 5.6)T  =  (-5.1, 4.8)T  =  w   (almost)

Next: Does v · u  =  0.0 ?

(5, 1)T · (-1.3, 5.6)T  =  -6.5 + 5.6  =  -0.9  =  0.0   (not quite)

QUESTION 13:

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