hw5sol - Winter 2011 • Math 67 • Linear Algebra...

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Unformatted text preview: Winter 2011 • Math 67 • Linear Algebra Homework 5 Problem A. Using the row reduction method, determine the set of solutions of the system of equation Ax = b where ( a ) A = 1 1 1- 1 2 , b = 2 2 ( b ) A = 1 10- 2 5- 3 4 2 1 , b = 20 8 6 ( c ) A = 1 1 1- 1 2 , b = 2 3 ( d ) A = 1 10- 2 1 5- 3 4 1 2 1 1 , b = 20 8 6 Remember, as you do the row reduction (no changing the columns!), your goal have a matrix that looks like 0 0 1 * * 0 0 * ... * 1 0 * ... * 1 * ... * . . . If you are strugling, do (b) and (d) first and then try the other two. Solution A(a). We row reduce 1 1 2 1- 1 0 2 2 -→ 1 0 1 0 1 1 0 0 0 . This implies that ( x 1 , x 2 ) where x 1 = 1 and x 2 = 1 is the only solution. 1 2 Solution A(b). We row reduce 1 10- 2 20 5- 3 4 8 2 1 6 -→ 1 0 0 2 0 1 0 2 0 0 1 1...
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This note was uploaded on 11/13/2011 for the course MATH 67 taught by Professor Schilling during the Winter '07 term at UC Davis.

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hw5sol - Winter 2011 • Math 67 • Linear Algebra...

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