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Final Exam - Ohio State University MATH 2568

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Math 2568 Summer 2020 Final Exam Testing guidelines •) Show all of your work. Correct answers with no supporting work may receive no credit. •) Circle or highlight your final answers. •) Yo... u may use your textbook and class notes. Problem Maximum Recorded Number Point Value Point Value Problem 1 10 Problem 2 10 Problem 3 10 Problem 4 10 Problem 5 10 Problem 6 10 Problem 7 12 Problem 8 16 Problem 9 11 Problem 10 15 Problem 11 16 Problem 12 10 Problem 13 10 Problem 14 10 Problem 15 10 Problem 16 10 Problem 17 10 Problem 18 10 Total 200 Problem 1 Let A =   3 1 5 7 −4 2 11 8 −3 12 13 9 10 −6 8  . a) [4 pts] Find a basis for N(A) in rational format. b) [3 pts] Find a particular solution to the matrix equation A ∗ x =   5 −2 14  . c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b). Problem 2 [10 pts] For a fixed matrices B, C ∈ R 2×2 , let W = {A ∈ R 2×2 | A ∗ B = 2A ∗ C}. Determine if W is a subspace of R 2×2 (either prove that it is, or show via specific counterexample that it isn’t). Problem 3 Let L : R 4 → R 3 be given by L     x1 x2 x3     =   (3x1 − 4x2 + 11x4) (15x2 + 9x3 − 21x4) (−6x1 + 9x2 + 4x3 − 5x4)  . a) [4 pts] Show that L is a linear transformation, and find the matrix representation A of L with respect to the standard bases for R 4 and R 3 . b) [3 pts] Use part a) to find a basis for ker(L). c) [3 pts] Use part a) for find a basis for im [Show More]

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