Solve the following system of IVP: [3 -1 0] 7 x' = Ax where A = 4 -2 0 and x(0) = |10 [4 -4 2] Hint: The eigenvalues are 11 = -1, 12 = 2, 23 = 2. 2

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A: Here we have to verify that λi  is an eigenvalue of A and that xi is a corresponding eigenvector .

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Q: Can step 2 be more elaborated upon? Specifically on how each eigenspace is found.

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A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…