wksht09sol - MATH 152 L1 & L2 Applied Linear...

Info iconThis preview shows pages 1–2. 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 152 L1 & L2 Applied Linear Algebra and Differential Equations Spring 2004-05 ¥ Week 09 Worksheet Solutions : Systems of Linear Equations Q1. (Method of reduction) Solve the system of linear equations x 1- 2 x 2 +2 x 3 = , 3 x 1- 6 x 2 +7 x 3 =- 1 , 2 x 1- 4 x 2 +3 x 3 = 1 . Solution We simplify the augmented matrix as follows 1- 2 2 3- 6 7- 1 2- 4 3 1 - 3 R 1 + R 2------→- 2 R 1 + R 3 1- 2 2 1- 1- 1 1 - 2 R 2 + R 1------→ R 2 + R 3 1- 2 2 1- 1 . Interpreted the last matrix (in reduced row echelon form) as a system of linear equations, we have x 1- 2 x 2 = 2 , x 3 =- 1 , = . The last equation is redundant. From the second equation, we have x 3 =- 1. From the first equation, we have x 1 = 2 + 2 x 2 . The system has non-unique solutions ( x 1 ,x 2 ,x 3 ) = (2 + 2 r, r,- 1) , for any arbitrary number r . Q2. (Method of reduction) Solve the system of linear equations - x 3- 3 x 4 +2 x 5 = 2 ,- 2 x 1 +4 x 2- 5 x 3 +7 x 4 + x 5 = 1 , x 1- 2 x 2 +3 x 3- 2 x 4 + x 5 = . Solution We simplify the augmented matrix as follows - 1- 3 2 2- 2 4- 5 7 1 1 1- 2 3- 2 1 2 R 3 + R 2-----→ R 1 ↔ R 3 1- 2 3- 2 1 1 3 3 1- 1- 3 2 2 - 3 R 2 + R 1------→ R 2 + R 3 1- 2- 11- 8- 3 1 3 3 1 5 3 1 5 R 3----→ 1- 2- 11- 8- 3 1 3 3 1 1 3 / 5 8 R 3 + R 1------→- 3 R 3 + R 2 1- 2- 11 9 / 5 1 3- 4 / 5 1 3 / 5 ....
View Full Document

This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.

Page1 / 4

wksht09sol - MATH 152 L1 & L2 Applied Linear...

This preview shows document pages 1 - 2. Sign up to view the full document.

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