MATH 204 Dec 2014 Final - CONCORDIA UNIVERSITY Department...

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CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Number Section(s) Mathematics 204 A Examination Date Pages Final December 2014 2 Instructors Course Examiners A. Sierpinska, S. Shi, E. Cohen S. Vassileva, R. Mearns Special Instructions . Only approved calculators are allowed. . Justify all your answers. . All questions have equal value. 1. Use the Gauss-Jordan method to find all the solutions of the system: 2 x 1 + 2 x 2 + 2 x 3 = 0 - 2 x 1 + 5 x 2 + 2 x 3 = 1 8 x 1 + x 2 + 4 x 3 = - 1 2. Determine the values of a for which the system has no solution, exactly 1 solution or infinitely many solutions: x + 2 y + z = 2 2 x - 2 y + 3 z = 1 x + 2 y - ( a 2 - 3) z = a 3. Find the inverse of A = 3 4 - 1 1 0 3 2 5 - 4 , if it exists. 4. (a) Evaluate the determinant of A = 2 1 3 1 1 0 1 1 0 2 1 0 0 1 2 3 . (b) Solve by Cramer’s rule, when it applies: x 1 + 2 x 3 = 6 - 3 x 1 + 4 x 2 + 6 x 3 = 30 - x 1 - 2 x 2 + 3 x 3 = 8
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