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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An equation whose highest variable exponent is 1 is called a what? My questions is actually about multistep equations I have 2 questions they are 1.2m+5=m over 5(in fraction form)-4,2. m over 2 (in fraction form)+3=m over 5 (in fraction form)+5