MA 405 Second Midsemester Quiz Solutions

MA 405 Second Midsemester Quiz Solutions - Lin Alg Matrices...

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Lin Alg & Matrices Second Midsemester Quiz Spring 1996 Your Name: For purpose of anonymous grading, please do not write your name on the subsequent pages. This examination consists of 5 questions, each question counting for the given number of points, adding to a total of 21 points. Please write your answers in the spaces indicated, or below the questions (using the back of the sheets if necessary). You are allowed to consult two 8 . 5 0 × 11 0 sheets with notes, but not your book or your class notes. If you get stuck on a problem, it may be advisable to go to another problem and come back to that one later. You will have 75 minutes to do this test. Good luck! Problem 1 2 3 4 5 Total If you are taking the exam later, please sign the following statement: I, , affirm that I have no knowledge of the contents of this exam. Signature 1
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Problem 1 (7 points): Please answer the following questions about vector spaces and matrices. Please, also justify your answers briefly. (a, 1.5pts) Consider R 2 with x 1 y 1 x 2 y 2 = x 1 + x 2 - y 1 - y 2 for addition and α fl x 1 y 1 = αx 1 αy 1 for scalar multiplication. Is R 2 with these operations a vector space?
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