Advanced Math

Advanced Math MATH 3341 Spring 2021 Exam 1, Part I VERSION A March 19, 2021 • This is part I of a two part exam. When I receive your solutions for part I by e-mail, then I will respond with a copy of Exam 1, Part II. • For each question in Part I, you will recieve + 10 points for all questions answered correctly. − 10 3 points for all questions answered incorrectly. 0 point for all questions left unanswered. • All answers should be sent to mail2MYL@fdu.edu. • Question number and letter answer must appear side by side. Here is an examples: VERSION A Q.1: a Q.2: unanswered Q.3: d 1 1. Find the rank of the following matrix   1 1 2 2 4 6 3 2 5 (a) 9 (b) 3 (c) 1 (d) none of the above 2 2. Find the inverse of    1 2 (a) 0 4   0 1 −1 (b) 4 −2 −4   4 0 1 (c) 4 −2 1 (d) none of the above 3 1 0 2 4  3. Let the position vector of a moving particle by r = r(t) = t i − t2 j + (t2 − 2 t) k, where t represent time. Find the velocity vector at the time when it passes through the point (2, −4, 0) (a) i + 4 j + 2 k (b) i − 4 j + 2 k (c) i − 4 j − 2 k (d) none of the above 4 4. Find det(AB) for the matrix matrix     4 2 1 2 A= B= 3 1 2 3 (a) +2 (b) +4 (c) +8 (d) none of the above 5 5. Find the distance between the points (1, 0, 1, 1, 0) and (−1, 0, −1, 1, −1) (a) +1 (b) +2 (c) +3 (d) none of the above 6 6. Find the derivative of −x y 2 + y z 2 at (2, 1, 1) in the direction of the vector i + j + k (a) 3 i + 2 j + k (b) -2 (c) 0 (d) none of the above 7 7. Consider the vector (−3, +9, −17). Write it as linear combinations of the vectors (−9, 0, −7) (0, −9, 13) (a) (b) (c) 4 (−9, 0, −7) + 91 (0, −9, 13) 9 4 (−3, +9, −17) − 91 (−9, 0, −7) 9 1 (−9, 0, −7) − (0, −9, 13) 3 (d) none of the above 8 8. If A = i − 3 j, B = i + j − 1 k, What is (C · B) A? (a) +3 (i + j − 1 k) (b) +3 (−3 j + i) (c) +2 (−3 j + i) (d) none of the above 9 C = i + j − 1 k. Advanced Math MATH 3341 Spring 2021 Exam 1, Part I VERSION A March 19, 2021 • This is part II of a two part exam. • For each question in Part II, you will recieve + 20 points for all questions answered correctly. This must include a complete derivation, and also a box around your answer. • All answers should scanned and sent to mail2MYL@fdu.edu in 1 pdf file. 1 1. For the linear combinations of the set of functions {ex , x ex } , either verify that it is a vector space, or show which requremenents are not satisfied. If it is a vector space, find a basis,and the dimension of the space. 2 R 2. Evaluate the line integral (x2 − y 2 ) dx − 2 x y dx dy along each of the following paths from (0, 0) to (1, 2). (a) y = 2 x2 (b) y = 0 from x = 0 to x = 2; then along the strait line joining (2,0) to (1,2). 3
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