Differential Equations: Given that λ1= 6, v1=(1,1) and λ2=−2, v2=(1−1) are eigenpairs of A, solve x′=Ax,...

Question

Question

Differential Equations:

Given that λ1= 6, v1=(1,1) and λ2=−2, v2=(1−1) are eigenpairs of A, solve

x′=Ax, x(0) =k.

(Ans:~x=(e6t)(3,3)+e^(−2t)(−6,6)) This is the answer but not sure how to get there.

math Advanced-Math

Answer 1

Answer #1

Given two eigen values and corresponding eigennectors 2. = 6, VIS (,1) 22= -2,72 = (1,-1). :. Solution will be x = 0,2** (1)

Answer 2

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