Consider the linear system A₁ = i ÿ' [ a. Find the eigenvalues and eigenvectors for the coefficient matrix. 16 V₁ 3 (-3-1)/5 -5 b. Find the real-valued solution to the initial value problem [31 โy ÿ. and X₂ = 3y₁ + 2y2, -5y₁ - 3y2, Use t as the independent variable in your answers. y₁ (t) = 7cost y2(t) = 15cos(t) + 5sin(t) = -i y₁ (0) = 7, Y₂ (0) = -15. 15 v₂ = = (-3+i)/5 1

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