MidtermSolutions

MidtermSolutions - Midterm Exam Solution Set Linear Algebra...

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Unformatted text preview: Midterm Exam Solution Set- Linear Algebra and Infinite Series Math 2J, Fall 2008 Date: 11/03/08 1 (1) (20 pts) a) (15 pts) Let A = 1 1 1 2 1 1- 2 2- 1 Find A- 1 . Use Gauss-Jordan reduction: 1 1 1 1 0 0 2 1 1 0 1 0- 2 2- 1 0 0 1 -→ ··· -→ 1 0 0- 1 1 0 1 0 1 / 3 1 / 3 0 0 1 2- 4 / 3- 1 / 3 b) (5 pts) Solve the linear system x 1 + x 2 + x 3 = 1 2 x 1 + x 2 + x 3 = 2- 2 x 1 +2 x 2- x 3 = 3 Using A- 1 from part a), we compute - 1 1 1 / 3 1 / 3 2- 4 / 3- 1 / 3 · 1 2 3 = 1 5 / 3- 5 / 3 = x 1 x 2 x 3 (2) (20 pts) Consider the following linear system of equations:- x 1- 2 x 2 +2 x 3 +4 x 4 = 0 x 1 + x 2- x 3 = 1- x 3 + x 4 = 0 x 1- x 4 =- 1 Use Cramer’s rule to find x 4 . First find det( A 4 ) =- 1- 2 2 1 1- 1 1- 1 1- 1 = 3 . Next, find det( A ) =- 1- 2 2 4 1 1- 1- 1 1 1- 1 = 5 ....
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MidtermSolutions - Midterm Exam Solution Set Linear Algebra...

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