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Unformatted text preview: MATH 102 SOLUTIONS TO HW #1 Section 1.3, problem 4. The correct row operation is c a { Row 1 } + { Row 2 } { Row 2 } . This pro duces the equivalent linear system: ax + by = f , ( d bc a ) y = g fc a . If ( d bc a ) 6 = 0 then the formula for y is: y = ( d bc a ) 1 ( g fc a ) . Of course the condition that the second pivot be zero (missing) is the same as saying that ( ad bc ) = 0. Section 1.3, problem 18. The answer is no , it is not possible. a) If ~x = ( x, y, z ) and ~ y = ( X, Y, Z ) are both solutions to A~x = b , then clearly so is ~ z = 1 2 ~x + 1 2 ~ y . b) Then they must also meet in the line joining these two points. Section 1.3, problem 30. First start with: u + v + w = 6 u + 2 v + 2 w = 11 2 u + 3 v 4 w = 3 We apply, in order, the sequence of row operations: (1) 1 { Row 1 } + { Row 2 } { Row 2 } (2) 2 { Row 1 } + { Row 3 } { Row 3 } (3) 1 { Row 2 } + { Row 3 } { Row 3 } to obtain the equivalent linear system: u + v + w = 6 v + w = 5 7 w = 14 1 2 One can now easily backsolve to find first that...
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 Fall '08
 SZYPOWSK
 Math, Linear Algebra, Algebra

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