Transcription of Exercises and Problems in Linear Algebra
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Exercises and Problems in Linear Algebra
Exercises and Problems in Linear AlgebraJohn M. ErdmanPortland State UniversityVersion July 13, 2014c 2010 John M. ErdmanE-mail 1. MATRICES AND Linear EQUATIONS1 Chapter 1. SYSTEMS OF Linear Answers to Odd-Numbered Exercises8 Chapter 2. ARITHMETIC OF Answers to Odd-Numbered Exercises14 Chapter 3. ELEMENTARY MATRICES; Answers to Odd-Numbered Exercises23 Chapter 4. VECTOR GEOMETRY Answers to Odd-Numbered Exercises29 Part 2. VECTOR SPACES31 Chapter 5. VECTOR Answers to Odd-Numbered Exercises38 Chapter 6. Answers to Odd-Numbered Exercises45 Chapter 7. Linear Answers to Odd-Numbered Exercises53 Chapter 8. BASIS FOR A VECTOR Answers to Odd-Numbered Exercises58 Part 3.
(a)Use Gaussian elimination to put the augmented coe cient matrix into row echelon form. The result will be 2 4 1 1 1 a 0 1 1 b 0 0 1 c 3 5where a= , b= , and c= . (b)Use Gauss-Jordan reduction to put the augmented coe cient matrix in reduced row echelon form. The result will be 2 4 1 0 0 d 0 1 0 e 0 0 1 f 3 5where d= , e= , and f= .
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