# Linear Algebra with Applications

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• davidvictor
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Name: Tuesday section time: Student ID: Math 20F - Linear Algebra - Winter 2003 Quiz #4 — February 11 (Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.) Let v 1 = 2 1 - 1 , v 2 = 2 0 2 , and v 3 = - 1 - 1 2 . Answer the following questions. (As usual, be sure to justifiy your answers). 1. Are v 1 , v 2 , v 3 linearly independent? 2. If not, show explicitly an example of how they are linearly dependent. 3. What is the dimension of Span ( v 1 , v 2 , v 3 )? ANSWER: If they are linearly dependent, there is a non-trivial solution to 2 2 - 1 1 0 - 1 - 1 2 2 x = 0 . We search for a non-trivial solution using row reduction: 2 2 - 1 0 1 0 - 1 0 - 1 2 2 0 1 0 - 1 0 2 2 - 1 0 - 1 2 2 0
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