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)