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4. (10 points) The parts of this question are unrelated. Show your work. Simplify your results. (a) (5 points) The eigenspaces of a matrix A are shown in the figure below. Find A 2-eigenspace (-3)-eigenspace (b) (5 points) A local soup kitchen is staffed by volunteers who cook or serve the food. Each week, 25% of the volunteer cooks switch to serving, and 15% of the volunteer servers switch to cooking. Model the scenario using a stochastic matrix. What will the fraction of volunteer cooks be if the trend continues