MATH 3A Midterm: Midterm1_3A_s2017
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MATH 3A Full Course Notes
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Friday april 21 2017, 00:00 00. 50 pm. There are 4 exercises, worth a total of 100 = 36 + 36 + 20 + 8 points. Provide computations and or explanations, unless stated otherwise. Exercise 1 (36 = 6 + 12 + 6 + 4 + 4 + 4 pts) Solution: (a) [ 1, 4, 1]t ; (b) (c) Exercise 2 (36 = 4 + 4 + 5 + 10 + 10 + 3 pts) For c r consider u1 = . Solution: (a) the vectors are not multiple of each other, so independent. (b) it is a plane through the origin. (c) 42u1 + 1296u2 + (42u1 1296u2) = 0, so dependent. (d) for c = 1/2. One has 3[1, 1, 1]t + [1, 2, 3]t + 2[1, 1/2, 0]t = 0. (e) for example, one can take. 3 2 2 (f) no, there are many options (free variables).
