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Spring 2003 - Buss' Class - Quiz 3

Spring 2003 - Buss' Class - Quiz 3 - Name Student ID...

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Name: Thursday section time: Student ID: Math 20F - Linear Algebra - Spring 2003 Quiz #3 — May1 (Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.) You must show your work in order to get credit for a problem. Label your answers clearly. Let u 1 = 1 0 1 , u 2 = 1 2 4 , u 3 = 4 2 1 , and u 4 = 1 2 1 , 1. Is u 1 , u 2 , u 3 a spanning set for R 3 ? Explain why or why not. 2. Is u 1 , u 2 , u 3 a basis for R 3 ? Explain why or why not. 3. Is u 1 , u 2 , u 3 , u 4 a spanning set for R 3 ? Explain why or why not. 4. Is u 1 , u 2 , u 3 , u 4 a basis for R 3 ? Explain why or why not. ANSWERS: 1. Yes, it is a spanning set. To prove this, you may do one of the following: (a) Form the matrix A = ( u 1 u 2 u 3 ) , put A in row echelon form and note that the row echelon form does not have any row of all zeros. Or, (b) Form
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