1 point We consider the following system of two second order linear differential equations: d² dt2 Question 1 where B =

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1 Point We Consider The Following System Of Two Second Order Linear Differential Equations D Dt2 Question 1 Where B 1 (48.9 KiB) Viewed 10 times

1 point We consider the following system of two second order linear differential equations: d² dt2 Question 1 where B = X1 X2 (1) The the eigenvalues A1, A2 of the matrix B in ascending order (A₁A2), are equal to: + Ba = 0, √1 = (1, (ii) Write the corresponding eigenvectors of the matrix B (1 corresponds to ₁ and 2 corresponds to X2 ) in their simplest form, such as their first component is 1: v₂ = (1, a1 6 12 0 28 a2 and = =(x1, x₂) T (iii) The general complex solution of this system has the form = where a1, a2 are arbitrary complex numbers. Find the solution of the system that also satisfies the initial conditions 21 (0) = 12,2 (0) 22. Namely, write the values of a1 and a2 for this solution: (t) = ₁e¹₁¹₁ + a2e²√√₂¹v₂