MATH122 Final: Final Exam Winter 2018
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Instructor: (cid:3) chun-hua guo (001) (cid:3) vijayaparvathy agasthian (c01/02) Instructions: full credit is awarded only for well-presented, correct solutions in which all of your work is shown. The marks allocated for each question are found to the left of the question: your solution and nal answer should appear on the right side pages in this exam booklet. 2x1 + 4x2 + x3 2x4 = 15. X1 2x2 + 4x3 8x4 = 3. If possible, nd conditions on a and b such that the following system has no solutions, exactly one solution, and in nitely many solutions, respectively. x + 2y + 2z = 5. If it is, nd a 1, the inverse of a. 3 1 (b) find all solutions to ax = . Find an invertible matrix u such that u a = r, with r being the reduced row-echelon form for a, and express u as a product of elementary matrices.
