Math_152_April_2005

Math_152_April_2005 - Be sure this exam has 4 pages THE...

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Be sure this exam has 4 pages. THE UNIVERSITY OF BRITISH COLUMBIA Sessional Examination - April 2005 MATH 152: Linear Systems Instructors(sesction): Burggraf(201), Cotar(202), Young(203), Anstee(204), Cytrynbaum(205), Froese(206), Yilmaz(207), Cheviakov(208). Special Instructions: You have 2.5 hours to complete the exam. No calculators or other electronics permitted. One formula sheet is allowed. You must show your work and explain your answers. 1. (15 points) Consider the plane P consisting of all points ( x, y, z ) that satisfy the equation 2 x + y + z = 2. Consider the line L a given by the equations a x + y = 3 y + 2 z = 1 (a) For what values of a , if any, is the line L a parallel to the plane P ? (b) Set a = 1 and find the intersection point of L 1 and the plane P . (c) Set a = 1 and find either the sine or the cosine of the angle between L 1 and the plane P ( the plane P and not the normal to the plane P ). Be sure to state which one you are giving (sine or cosine). 2. (12 points) Consider the system of equations: x + y = 2, - x + y + z = 0, 2x + y = 1. (a) If the system is rewritten as A x = b , what are A and b ?

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