Question: Problem 8. (10 points) NOTE: Make sure you neatly write your work on paper. Do not skip steps. Label the different parts of the problem.

Problem 8. (10 points) NOTE: Make sure you neatly write your work on paper. Do not skip steps. Label the different parts of the problem. Remaining Consider the linear system = 6y1 + 4y2 = -12y1 - 8y2 a. Find the eigenvalues and associated eigenvectors of the coefficient matrix. 11 =, 31 = 18 1 b. Use the eigenvalue/eigenvector pairs from part (1) to find two linearly independent solutions of the system. Use t as the independent variable in your answe y (1) (t ) = c. Determine the solution to the system with initial conditions y1 (0) = 5, y2(0) - -6. y1(t) = y2 (t) =

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