14add_2 - r a 1 2 du r r 1 Consider the equation = 0 a 3 u = Au dt 0 0 a r r T subjected to the initial condition u(0 = uo = 0 0,1 1a What are the

14add_2 - r a 1 2 du r r 1 Consider the equation = 0 a 3 u...

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1.Consider the equation 120300aduauAudta==rrrsubjected to the initial condition [](0)0,0,1Touu==rr1a What are the eigenvalues of A? How many linear independent eigenvectors can you find? . . 29 Solve (1) with the given initial condition (express your answer in terms of the constant a1e. What is the solution of (1) if 1203 ,00aAbabcc=? ). Hint: The solution has the form: 12AtAtuecec=+rrrwhere 2()cN AbI-rand (29(21cNAaI-r. Write (AI tAteeeλλ-=. Find 1crand 2crusing the initial condition [](0)0,0,1Touu==rr. It 1b. Direct calculation shows that

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