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Linear systems: Problem 8 (15 points) Suppose that the matrix A has the following eigenvalues and eigenvectors:

`\lambda _(1)=5+3i with vec(v_(1))=[[-3],[5-4i]]`

and

`\lambda _(2)=5-3i with vec(v)_(2)=[[-3],[5+4i]]`

Write the general real solution for the linear system

`vec(r^('))=vec(A)`

, in the following forms: A. In eigenvalue/eigenvector form: B. In fundamental matrix form: [[x(t)],[y(t)]]=[[##],[vdots:]][[c_(1)],[c_(2)]] C. As two equations: (write "c1" and "c2" for c_(1) and c_(2) ) x(t) y(t) Note: if you are feeling adventurous you could use other eigenvectors like 4vec(v_(1)) or -3vec(v_(2)).