Linear Algebra, Solutions Manual

Ideas and Applications

Richard C. Penney

• Publisher: Wiley
• Year: 2015
• ISBN:
  9781118911839
• Edition: 4
• Topic: Mathematics
• Subtopic: Linear Algebra
• Index: Mathematics

This Student Solutions Manual to Accompany Linear Algebra: Ideas and Applications, Fourth Edition contains solutions to the odd numbered problems to further aid in reader comprehension, and an Instructor's Solutions Manual (inclusive of suggested syllabi) is available via written request to the Publisher. Both the Student and Instructor Manuals have been enhanced with further discussions of the applications sections, which is ideal for readers who wish to obtain a deeper knowledge than that provided by pure algorithmic approaches.

Linear Algebra: Ideas and Applications, Fourth Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, this book successfully helps readers to understand not only how to implement a technique, but why its use is important.

CHAPTER 1
SYSTEMS OF LINEAR EQUATIONS

1.1 THE VECTOR SPACE OF m × n MATRICES

Problems begin on page 17

EXERCISES

1. 1. 
      , [3, 0, −3, −6],
      
   2. 
      , [9, 72],
      
   3. 
      , [ − 1, 0],
      

3. C = A + B.

5. 1. 
   2. 
   3. 
   4. 
6. P₂ = P₅ − P₁ − P₃ − P₄, where P_i is the ith row of P.

9. Each vector has a nonzero entry in the positions where the other two vectors have zeros.
10. Suppose first that

    

    Then

    

    Equating entries yields the system

    

    From the first equation, x = 0. It then follows from the second equation that y = 0, which is impossible due to the third equation. Thus the independence is proved.

12. [1, −1, 0], [1, 0, 0], [2,...