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Unformatted text preview: Linear Algebra 040b Final Examination Saturday, April 14, 2007 1. [ 2 marks ] Let be the angle between the vectors (1 , 2 , 3) and (3 , 3 , 1). Find cos( ). 2. [ 4 marks ] Let ` be the line in R 3 passing through the points (2 , 4 , 1) and (4 , , 7). (a) Find parametric equations for ` . (b) Find the point of intersection of ` with the xyplane. 3. [ 8 marks ] Find (if possible) the conditions on a, b and c for which the following system of equations has no solution, one solution and infinitely many solutions. x y + 3 z = a y + z = b x + 4 z = c (Note: you do not have to find actual solutions.) 4. [ 8 marks ] Let W = Span( S ) where S = 1 2 1 , 2 3 1 3 , 1 2 2 , 1 4 1 2 . Find a subset of S which is a basis of W ....
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This note was uploaded on 04/18/2008 for the course LINEAR ALG 040 taught by Professor Dillhion during the Spring '08 term at UWO.
 Spring '08
 Dillhion

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