book Maths Puzzle Numerical Ability

How do you find eigenvectors? Can find eigenvalues but coming up with the vectors after the system has been solved, is eluding me. Need step by step instruction.

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book Other Question

A takes 32 sec to go around a circular track,B takes 24 sec and C takes 18 sec.If all starts from at the same time,in the same direction and from the same point,then after how much time will they be together again.
op:
a) 192 s
b)288 s
c) 32 s
d) 16 s
e) 252 s If a 17-ft. ladder is leaning against a building. The base of the ladder is 7 feet from the base of the building. How high up the side of the building is the top of the ladder?