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00aut-m2 - MATH 51 MIDTERM 2 Levandosky 11 15 11:00 1:15...

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MATH 51 MIDTERM 2 November 16, 2000 Brumfiel Hutchings Levandosky Staffilani White 11:00 01 05 09 13 17 1:15 03 07 11 15 19 Name: Student ID: Signature: Instructions: Print your name and student ID number and write your signature to indicate that you accept the honor code. Circle the number of the section for which you are registered on Infopier. During the test, you may not use notes, books, or calculators. Read each question carefully, and show all your work. Put a box around your final answer to each question. You have 90 minutes to do all the problems. Question Score 1 2 3 4 5 6 7 8 9 10 Total 1. (a) Compute the inverse of the matrix 1 3 - 2 0 2 4 0 0 - 1 1
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(b) For which value(s) of x is the matrix below not invertible? Explain your answer. 1 1 1 0 1 2 5 x 6 2. (a) Suppose A = 2 / 3 - 1 / 3 2 / 3 2 / 3 2 / 3 - 1 / 3 - 1 / 3 2 / 3 2 / 3 is the matrix of a linear transformation which is geometrically a 60 degree rotation about a line L in R 3 . Find the matrix of a 120 degree rotation about L . Hint: Think about composition.
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