Problem 7. For distinct real numbers λ, µ consider the matrix (62). Show that A = = (1) and (₁²1) are both eigenvectors of A. (b) Find the solution y(t) to the initial value problem y' = Ay; y (0) = (i). (c) Considering λ and t as fixed, use l'Hôpital's rule to calculate the limit z(t) = lim y(t) μ→1 of your solution to (b) as u →A and the system acquires a double root. (d) Write down a fundamental pair of vector solutions to the following matrix equation with a double eigenvalue: y = (1₂¹) y. y'

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