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ProblemSet6 Solutions

# ProblemSet6 Solutions - Department of Economics Ryerson...

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Department of Economics Ryerson University ECN230-Mathematics For Economics Problem Set #6 - Solutions EXERCISE 5.1 Problem 5: (a) Interchange row 2 and row 3 in A to get a matrix A 1 . In A 1 keep row 1 as is, but add row 1 to row 2, to get a matrix A 2 . In A 2 , divide row 2 by 5. Then multiply the new row 2 by 3, and ass the result to row 3. Finally, multiply row 3 by 5 42 . The resulting echelon matrix: A 3 = 1 5 1 0 1 1 5 0 0 1 contains three nonzero rows. Hence, r ( A ) = 3. (b) Interchange row 1 and row 3 in B to get a matrix B 1 . In B 1 , divide row 1 by 6. Then multiply the new row 1 by 3, and add the result to row 2, to get B 2 . In B 2 , multiply row 2 by 2, then add the new row 2 to row 3. The resulting echelon matrix: B 3 = 1 1 6 0 0 1 4 0 0 0 has two nonzero rows. Hence, r ( B ) = 2. There is linear dependence in B : v 0 1 = v 0 3 2 v 0 2 . Matrix B is singular. (c) Interchange row 2 and row 3 of matrix C , to get matrix C 1 . In C 1 , divide row 1 by 7. Then, multiply the new row 1 by 8, and add the result to row 2, to get

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