Please solve complete problem. I need complete step by step solution. Book: Fundamentals of differential equations.

2. Let x denote the &* column of a matrix . Write down a matrix A withe; =00 2]T ,ca=[101]",e5=[012]7. Recall that T denotes the transpose. {a) Without computing the characteristic polynomial of A, determine if the following vectors are eigenvectors of A, If yes, determine the correspond- ing eigenvalue. The vectors are [I 1 17, [1 1 1]7 and [1 2 4]7. (b) Use (a) or some other method to write down a fundamental matrix for the differential equation x'(f) = Ax(t). () Solve the initial value problem x'(t) = Ax(t), x(0) = [1 01]". (d) Give an example of a 3 x 1 non-constant vector that is not a solution of the initial value problem in (c). Prove that it is not a solution