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write the definition of (0.5 mark); then prove that (f(n) = n3 when f(n) = 5n3 + 2n2-4. FindCo.c1,no. (1.5 marks) 1. Find (n) for the following recurrence for the running time: 2.1 T(n)-aT(n-1) + 1 2. 2.2 T(n) = 3T() + 1 2.3 Tn)-)+1 (0.75 marks) (0.75 marks) (0.75 marks) 3 In Chapter 4 of our reference book (Introduction to algorithms), read Strassen's algorithm for matrix multiplication and answer the following questions. 3.1 Write the recurrence for the running time of Strassen's algorithm and find its . (0.5 marks) 3.2 Use the algorithm to compute the matrix product: 7 4(5 3 1 32 5 Show your work. (0.25 marks)