Suppose that A is 2×2 matrix with eigenvectors V1 = [2, -3], V2 = [1, 2] which correspond to ?1 = 3, ?2 = 2 respectively. Find the general solution to the system X' = AX. y = c1e^3t[2, -3] + c2e^2t[1, 2] y = c1e^3t[2, -3] + c2te^2t[1, 2] y = c1e^3t[2, -3] + c2e^2t{[1, 2] + t[2, -3]} none y = c1e^2t[2, -3] + c2e^3t[1, 2]
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In this case, we have v1 = [3] and λ1 = 3, and v2 = [1 2] and λ2 = 2. Therefore, the general solution to the system X' = AX is: X = c1[3]e3t + c2[1 2]e2t Show more…
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