It wants you to first find the characteristic polynomial. This is found by doing .
Normally this would be the way to do it however, you've already found the eigenvalues. The eigenvalues are the roots of the characteristic polynomial. Therefore the characteristic polynomial is .
In the case of the four column vectors it's important to notice that since you're dealing with and you have 4 vectors which span. As a result one of the vectors must be a linear combination of the others.
Sifting the vectors gives a,c and d. b is removed because it is or -2a (ie. a linear combination of a vector you already have as part of your basis).