ProblemSet4 Solutions

ProblemSet4 Solutions - Department of Economics Ryerson...

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Department of Economics Ryerson University ECN230-Mathematics For Economics Problem Set #4 - Solutions EXERCISE 5.1 Problem 3: (a) Yes. (b) Yes. (c) Yes. (d) No: v 0 2 = 2 v 0 1 . Problem 4: We obtain exactly the same results as in the preceding problem. EXERCISE 5.2 Problem 1: (a) 6 (b) 0 (c) 0 (d) 157 (e) 3 abc a 3 b 3 c 3 (f) 8 xy +2 x 30 Problem 2: +, ,+ , , . Problem 3: Minors: | M a | = ¯ ¯ ¯ ¯ af hi ¯ ¯ ¯ ¯ , | M b | = ¯ ¯ ¯ ¯ df gi ¯ ¯ ¯ ¯ , | M f | = ¯ ¯ ¯ ¯ ab gh ¯ ¯ ¯ ¯ 1
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Cofactors: | C a | = | M a | , | C b | = | M b | , | C f | = | M f | Problem 4: (a) 72 (b) 81 Problem 5: The cofactor of element 9 is: ¯ ¯ ¯ ¯ ¯ ¯ 23 4 16 0 0 50 ¯ ¯ ¯ ¯ ¯ ¯ =20 Problem 6: First, f nd the minors: | M 31 | = ¯ ¯ ¯ ¯ 11 4 27 ¯ ¯ ¯ ¯ = 69, | M 32 | = ¯ ¯ ¯ ¯ 94 37 ¯ ¯ ¯ ¯ = 51, | M 33 | = ¯ ¯ ¯ ¯ 91 1 32 ¯ ¯ ¯ ¯ = 15 Since a cofactor is simply the minor with a particular sign, according to | C ij | =( 1) i + j | M ij | we f nd: | C 31 | 1) 3+1 | M 31 | =69 | C 32 | 1) 3+2 | M 32 | = 51 | C 33 | 1) 3+3 | M 33 | = 15 Problem 7: Perform cofactor expansion for the second column: | A | = a 12 | C 12 | +
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This homework help was uploaded on 04/18/2008 for the course ECONOMICS ECN 230 taught by Professor Angrydis during the Winter '08 term at Ryerson.

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ProblemSet4 Solutions - Department of Economics Ryerson...

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