MATH 3A Midterm: Midterm2_3A_w2018
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MATH 3A Full Course Notes
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There are 4 exercises, worth a total of 40 points. Provide computations and or explanations, unless stated otherwise. Exercise 1 (13 = 2 + 2 + 3 + 2 + 1 + 2 + 1 pts ) Solution: (a) x2 x 2 = (x 2)(x + 1). (b) x 6= 2, 1. (c) 0 (d) {[ 1, 1, 1]t }. (e) 1. (f) {[1, 0, 1]t , [0, 2, 2]t }. (g) 2. Exercise 2 (6 = 2 + 2 + 2 pts) (a) compute the matrix product. 1 2 (b) find a matrix x such that (cid:20) 1 2. 1 0 1 (cid:21) + 2x t = 0. 3 (c) find a nonzero 2 2 matrix a with a2 = 0. Exercise 3 (11 = 2 + 1 + 4 + 2 + 2 pts) If so, nd a diagonal matrix d and an invertible ma- trix p such that a2018 = p d p 1.
