# Linear Algebra with Applications

 General Information Syllabus Homework Assignments Exam Related Class Material

## Homework assignments

Homework assignments are to be handed in weekly. In general, assignments for a given week are to be submitted in class next Wednesday.

Answer Key for the homework assigned for November 15 – November 22 is now available.
Answer Key for the homework assigned for November 8 – November 12 is now available.
Answer Key for the homework assigned for November 1 – November 5 is now available.
Answer Key for the homework assigned for October 25 – October 29 is now available.
Answer Key for the homework assigned for October 18 – October 22 is now available.
Answer Key for the homework assigned for October 11 – October 15 is now available.
Answer Key for the homework assigned for October 4 – October 8 is now available.
Answer Key for the homework assigned for September 22 – October 1 is now available.

Week of November 29 – December 1, 2004

 Monday, November 29: Study: Chapter 5, Section 7. Do written assignment (not to be handed in, will not be graded): Section 5.7 problems 2, 4, 6, 8 (p. 361).

Week of November 22 – November 26, 2004

 Monday, November 22: Study: Chapter 6, Section 3. Do written assignment (due Monday, November 29, at the end of the lecture): Section 6.3 problems 2, 6, 10, 12, 16, 18, 24 (pp. 400, 401).

Week of November 15 – November 19, 2004

 X-hour Thursday, November 18 and Friday, November 19: Study: Chapter 6, Section 2. Do written assignment (due Monday, November 29, at the end of the lecture): Section 6.2 problems 6, 10, 14, 16, 20, 34 (pp. 392, 393). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 6.2 problems 27, 33 (p. 393).
 Wednesday, November 17: Study: Chapter 6, Sections 1 and 7. Do written assignment (due Monday, November 29, at the end of the lecture): Section 6.1 problems 2, 16, 18, 30 (pp. 382, 383) and Section 6.7 problems 4, 6, 14, 18 (pp. 435, 436). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 6.1 problems 25, 27, 31 (p. 383) and Section 6.7 problems 13 (p. 436).
 Monday, November 15: Study: Chapter 5, Section 4. Do written assignment (due Monday, November 29, at the end of the lecture): Section 5.4 problems 4, 6, 8, 10, 12, 16 (pp. 333, 334). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 5.4 problems 17, 25 (p. 334).

Week of November 8 – November 12, 2004

 Friday, November 12: Study: Chapter 5, Section 3. Do written assignment (due Wednesday, November 17, at the end of the lecture): Section 5.3 problems 10, 14 (please note that the eigenvalues for this matrix are given at the end of page 325), 20, 26, 28 (pp. 325, 326).
 Wednesday, November 10: Study: Chapter 5, Section 3. Do written assignment (due Wednesday, November 17, at the end of the lecture): Section 5.3 problems 2, 4, 6, 8, 16 (please note that the eigenvalues for this matrix are given at the end of page 325), 24, 32 (pp. 325, 326). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 5.3 problems 25, 29, 31 (p. 326).
 Monday, November 8: Study: Chapter 5, Section 2. Do written assignment (due Wednesday, November 17, at the end of the lecture): Section 5.2 problems 4, 10, 12, 16, 20, 24 (pp. 317, 318). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 5.2 problems 19, 23 (p. 318).

Week of November 1 – November 5, 2004

 Friday, November 5: Study: Chapter 5, Section 1. Do written assignment (due Wednesday, November 10, at the end of the lecture): Section 5.1 problems 2, 6, 8, 12, 18, 24, 32 (pp. 308, 309). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 5.1 problems 23, 25, 27, 31 (p. 309).
 Thursday, November 4: Study: Chapter 4, Section 6. Do written assignment (due Wednesday, November 10, at the end of the lecture): Section 4.6 problems 2, 6, 10, 14, 20, 24 (pp. 269, 270). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 4.6 problems 7, 19 – 25 (pp. 269, 270).
 Wednesday, November 3: Study: Chapter 4, Section 5. Do written assignment (due Wednesday, November 10, at the end of the lecture): Section 4.5 problems 2, 8, 12, 14, 22 (you don't need to know anything about properties of the Laguerre polynomials, what they are used for, or why they are called that way), 24, 26 (pp. 260, 261). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 4.5 problems 9, 25, 27 (pp. 260, 261).
 Monday, November 1: Study: Chapter 4, Section 4. Do written assignment (due Wednesday, November 10, at the end of the lecture): Section 4.4 problems 4, 8, 10, 14, 22 (have a look at problem 21 first), 26, 30, 32 (pp. 254, 255). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 4.4 problems 19, 21, 23 – 25, 31 (pp. 254, 255).

Week of October 25 – October 29, 2004

 Wednesday, October 27: Study: Chapter 4, Section 3. Do written assignment (due Wednesday, November 3, at the end of the lecture): Section 4.3 problems 2, 6, 10, 12, 14, 34 (pp. 243 – 245).
 Monday, October 25: Study: Chapter 4, Sections 2 and 3. Do written assignment (due Wednesday, November 3, at the end of the lecture): Section 4.2 problems 32, 34 (pp. 235, 236) and Section 4.3 problems 4, 8, 16, 20, 24, 26 (pp. 243, 244). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 4.2 problems 31, 33, 35 (pp. 235, 236) and Section 4.3 problems 23, 25 (p. 244).

Week of October 18 – October 22, 2004

 Friday, October 22: Study: Chapter 4, Sections 1 and 2. Do written assignment (due Wednesday, October 27, at the end of the lecture): Section 4.1 problems 12, 16, 22 (pp. 223, 224) and Section 4.2 problems 2, 6, 8, 10, 18, 22, 24 (pp. 234, 235). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 4.1 problems 21, 31 (pp. 224, 225).
 Wednesday, October 20: Study: Chapter 3, Section 2 and Chapter 4, Section 1. Do written assignment (due Wednesday, October 27, at the end of the lecture): Section 3.2 problems 6, 12, 24, 32, 34, 42 (pp. 199, 200) and Section 4.1 problems 2, 6, 8 (here denotes the set of of polynomials of degree at most n, see Example 4, page 218), 30 (pp. 223 – 225). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 3.2 problems 31, 35 (p. 200) and Section 4.1 problems 1, 3, 25 – 29 (pp. 223, 224).
 Monday, October 18: Study: Chapter 3, Section 1 and 2. Do written assignment (due Wednesday, October 27, at the end of the lecture): Section 3.1 problems 2, 6, 10, 14, 22, 30, 36 (pp. 190, 191).

Week of October 11 – October 15, 2004

 Friday, October 15: Study: Chapter 2, Section 3. Do written assignment (due Wednesday, October 20, at the end of the lecture): Section 2.3 problems 4, 6, 14, 18, 28 (use comment and (slightly modified) hint from exercise 27), 34, 38 (pp. 132, 133). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 2.3 problems 15, 17, 37 (pp. 132, 133).
 Wednesday, October 13: Study: Chapter 2, Section 2. Do written assignment (due Wednesday, October 20, at the end of the lecture): Section 2.2 problems 18, 24, 30, 32, 34 (for n = 3 and 4 only), 38 (pp. 126, 127). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 2.2 problems 17, 19, 21 – 23 (pp. 126, 127).
 Monday, October 11: Study: Chapter 2, Section 1 and 2. Do written assignment (due Wednesday, October 20, at the end of the lecture): Section 2.1 problems 6, 22 (Hint: if columns are linearly dependent, then there should exist a non-trivial linear combination of them that is zero. Use it), 24, 32 (Hint: figure out first how Ae_i, where e_i is the i-th basis vector, is related to columns of A. Consider a couple of examples before making a statement) (pp. 116, 117) and Section 2.2 problems 4, 6, 14, 26 (pp. 126, 127). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 2.1 problems 18 – 21, 23, 25, 31 (pp. 116, 117) and Section 2.2 problems 13, 25 (pp. 126, 127).

Week of October 4 – October 8, 2004

 X-hour Thursday, October 7 and Friday, October 8: Study: Chapter 1, Sections 8, 9 and Chapter 2, Section 1. Do written assignment (due Wednesday, October 13, at the end of the lecture): Section 1.8 problem 32 (p. 81); Section 1.9 problems 2, 4, 8, 12, 18, 22, 26 (pp. 90, 91); Section 2.1 problems 2, 10 (p. 116). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 1.8 problems 25, 29 (p. 81); Section 1.9 problems 11, 13, 25 – 28, 29, 35 (pp. 90, 91).
 Wednesday, October 6: Study: Chapter 1, Sections 7 and 8. Do written assignment (due Wednesday, October 13, at the end of the lecture): Section 1.7 problems 8, 14, 18, 32 (hint: you don't need to reduce the matrix to an Echelon Form) (pp. 71, 72), Section 1.8 problems 6, 10, 12, 20 (p. 80). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 1.8 problems 7, 8, 13 – 16 (p. 80).
 Monday, October 4: Study: Chapter 1, Section 5 and 7. Do written assignment (due Wednesday, October 13, at the end of the lecture): Section 1.5 problems 16 (use your solution for problem 6 from the previous homework), 18, 30, 36 (pp. 55, 56); Section 1.7 problems 2, 10, 16, 24, 28 (pp. 71, 72). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 1.5 problems 19 – 22, 25, 35, 37 (pp. 55, 56); Section 1.7 problems 23 – 26, 31 (pp. 71, 72).

Week of September 27 – October 1, 2004

 Friday, October 1: Study: Chapter 1, Sections 4 and 5. Do written assignment (due Wednesday, October 6, at the end of the lecture): Section 1.4 problems 8, 12, 14, 16, 18, 22, 32 (pp. 47 – 49) and Section 1.5 problems 6, 14, 28 (pp. 55, 56). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 1.4, problems 1, 3, 13, 15, 19, 31, 33 (pp. 47 – 49). and Section 1.5 problems 1, 13, 17, 27 (pp. 55, 56).
 Wednesday, September 29: Study: Chapter 1, Section 3. Do written assignment (due Wednesday, October 6, at the end of the lecture): Section 1.3 problems 8, 10, 12, 14, 18, 26, 30 (pp. 37 – 39). Problems to practice (do not hand in solutions to these problems, they will not be graded): Section 1.3 problems 5, 15, 19, 21, 25 (pp. 37, 38).
 Monday, September 27: Study: Chapter 1, Section 2. Do written assignment (due Wednesday, October 6, at the end of the lecture): Section 1.2 problems 12, 14, 28 (don't forget to explain your answer), 31 (p. 25, 26).

Week of September 22 – September 24, 2004

 Friday, September 24: Study: Chapter 1, Sections 1 and 2. Do written assignment (due Wednesday, September 29, at the end of the lecture): Section 1.1 problems 18, 20, 32 (pp. 11, 12); Section 1.2 problems 2, 4, 6 (don't forget to explain why you listed all the echelon forms possible), 10, 16, 20, 24 (pp. 25, 26). Problems to practice (do not hand in solutions to these problems, they will not be graded): Try to (correctly) answer as many questions from problems 23–31 (p. 26) as possible.
 Wednesday, September 22: Study: Chapter 1, Section 1. Do written assignment (due Wednesday, September 29, at the end of the lecture): Section 1.1 problems 4, 12, 16 (p. 11).