sampleexam1

# sampleexam1 - 0 5-2 8 4-1 3-6 1-2 1 0 5-2 8 0 7-1-6 4...

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MAS 3114, Fall 10, Exam 1 No Calculators, books, or notes. 1. True/False: Mark each of the following as either True or False. No explanation required. 1. In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. 2. An inconsistent system has more than one solution. 3. When u, v R 3 are non-zero vector, Span( { u, v } ) contains the line through u and the origin. 4. The equation Ax = b is consistent if the augmented matrix [ A | b ] has a pivot position in every row. 5. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. 2. Find h and k so that the system with augment matrix 1 3 2 5 h k has (a) no solution; (b) many solutions. 3. Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. 1

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Unformatted text preview: 0 5-2 8 4-1 3-6 , 1-2 1 0 5-2 8 0 7-1-6 . 4. Suppose the augmented matrix [ A | u ] is row equivalent to B = 1 0 0 2 0 1 0 3 0 0 1 5 0 0 0 0 . 1 • Is u in the span of the columns of A ? • Do the columns of A span R 4 ? 5. Suppose C is row equivalent to D = 1 1 0 0 0 0 0 1 2 0 0 0 0 0 1 • Do the columns of C span R 3 ? • Can every vector in R 3 be written as a linear combination of the columns of C ? 6. A mining company owns two mines. Mine 1 produces 20 tons of copper and .11 tons of silver per day; and mine 2 produces 30 tons of copper and .1 tons of silver per day. Let x j denote the number of days mine j operates. Write a system of equations whose solution gives the number of days each mine should operate to produce 150 tons of copper and .6 tons of silver. 2...
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