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G canvas.ucsc.edu Fa.. Untitled document... ICSC Cover Letters Ucsc https://careers.ucsc... UCSC https://careers.ucsc... T how to get answers.. day arter (a) (2 pts) Suppose that Ak, BE, and Ck are the percentages of the Cheggers fleet at each of ements the three lots (Airport, Broadway and Calvin, respectively) at the beginning of day k (before any cars are rented for the day). Find the system of linear equations that describes how the ons percentages at the beginning of day k+1, Ax+1, Bx41, and C+1, depend on the percentages on day k, Ak, Bk, and Ck, and express this relationship in the form Fx+1 = M . Fx, where M is a 3 x 3 matrix and Ak FK = BK ccess (b) (3 pt) Explain (briefly) why 2 = 1 is an eigenvalue of M, and find an eigenvector of M with this eigenvalue. Show your work, including at least two intermediate matrices in the Gaussian elimination process. (c) (2 pts) Find the other eigenvalue(s) of M. You do not need to find corresponding eigenvector(s). On January 1st, 2022, before any cars are rented, Ao = 50%, Bo = 25%, and Co = 25% . (d) (3 pts) Based on your answer to part (b), estimate the percentages of cars in each of the four lots at the beginning of January 1, 2023. Explain the reasoning, including why your work on part (c) is not important for this estimate. For full (or any) credit, show your work and explain your reasoning. No Matlab Edit View Insert Format Tools Table 12pt Paragraph B IU AV & TV : MacBook Pro @ $ % & 2 3 4 5 6 7 8