102_solutions1

102_solutions1 - MATH 102 SOLUTIONS TO HW #1 Section 1.3,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 back-solve to find first that...
View Full Document

Page1 / 4

102_solutions1 - MATH 102 SOLUTIONS TO HW #1 Section 1.3,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online