Question: This is an example of the district real roots case. x = Ax where A = (1) Find the characteristic polynomial p(A) of A, then

This is an example of the "district real roots case".

x = Ax where A = (1) Find the characteristic polynomial p(A) of A, then use this polynomial to determine the eigenvalues of A. (2) In this case there are two eigenvalues A, and A2. For each eigenvalue A; find an associated eigen vector vi (each eigenspace will be one dimensional in this case). (3) Write down your general solution: x(t) = Ciev, + Czekalva. (4) Solve the initial value problem: (i) x' = Ax (ii) x(0) = -2

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