SPRING 2008

Math 215: Linear Algebra, Sections 1 and 3.

Homework:

• Homework 1 - due 1/18
  Exercises 1.1: 5, 18, 22; Exercises 1.2: 4, 10.
• Homework 2 - due 1/23
  Exercises 1.2: 16, 25, 36, 43, 59; Exercises 1.3: 2, 4; extra credit-- problem on projection of a vector onto a plane
• Homework 3 - due Friday 1/25
  Exercises 1.3: 10, 14, 18, 24, 28, 38, 40.
• Homework 4 - due Monday 1/28
  Exercises 2.1: 16, 28 & 34, 32, 40; Exercises 2.2: 16, 18.
• Homework 5 - due Wednesday 1/30
  Exercises 2.2: 14, 28, 36, 42.
• Homework 6 - due Friday 2/1
  Exercises 2.2: 24, 30 (Use Gauss-Jordan), 40, 48; Exercises 2.3: 4, 8.
• Homework 7 - due Monday 2/4
  (Note: This is when the material becomes theoretical, and questions becomes proof-oriented.)
  Exercises 2.3: 12, 24, 34, 43, 44.
• Homework 8 - due Wednesday 2/6
  Exercises 2.4: 12, 16, 24, 25, 27.
• Homework 9 - due Monday 2/11
  Exercises 3.1: 1, 6, 22, 29, 32.
• Homework 10 - due Wednesday 2/13
  Exercises 3.1: 8, 26, 28; Exercises 3.2: 8, 22, 36.
• Homework 11 - due Friday 2/15
  Exercises 3.2: 10, 14, 42; Exercises 3.3: 12, 17, 22.
• Homework 12 - due Monday 2/18
  Exercises 3.3: 19, 26, 40, 42, 46, 52.
• Homework 13 - due Wednesday 2/20
  Exercises 3.3: 47 (warning: DO NOT ASSUME the inverses of A and B exist!!); Exercises 3.4: 4, 10, 18, 29.
• Homework 14 - due Friday 2/22
  Exercises 3.4: 24, 28, 30; Exercises 3.5: 6, 8, 12.
• Homework 15 - due Monday 2/25
  Exercises 3.5: 10, 14, 16, 18 (not null(A)), 28 (keep them as columns of the matrix and use procedure for column space, or turn them into rows and use procedure for row space), 46.
• Homework 16 - due Wednesday 2/27
  Exercises 3.5: 18 (null(A)), 36, 42, 44, 56, 57.
• Homework 17 - due Friday 2/29
  Exercises 3.6: 9, 18, 32, 36, 40, 54.
• Homework 18 - due Monday 3/3
  Exercises 3.7: 10, 12, 13, 14.
• Homework 19 - due Wednesday 3/5
  Exercises 3.7: 24 (Just set up the Leslie matrix and find population for the year 1991), 28, 30, 34, 38, 52(a,b,c).
• Homework 20 - due Monday 3/10
  Exercises 4.1: 6, 12, 14, 20, 24, 37.
• Homework 21 - due Wednesday 3/12
  Exercises 4.2: 8, 25, 28, 30, 36, 40, 46, 48.
• Homework 22 - due Friday 3/15
  Exercises 4.2: 60, 66 (Hint: Use inverse of A); Exercises 4.3: 6, 19, 20, 25.
• Homework 23 - due Monday 3/24
  Exercises 4.3: (17+18), 34 (use calculator to compute the powers), 36, (24+41); Exercises 4.4: 2, 6, 8, 26, 34, 41, 42, 45.
  Note: None of these proofs take more than a couple lines.
• Homework 24 - due Wednesday 3/26
  Exercises 4.3: 40 (just do it for 3x3 matrices), 41 (use result from 40 for nxn matrices); Exercises 4.4: 22; Exercises 4.6: 58, 64, 67+70.
• Homework 25 - due Friday 3/28
  Exercises 4.6: compute e^A for matrix in problem 78; 80, 86, 88.
• Homework 26 - due Monday 3/31
  Exercises 6.1: 6, 10, 38, 46, 47, 62.
• Homework 27 - due Wednesday 4/2
  Exercises 6.2: 2, 8, 12, 17, 24, 28.
• Homework 28 - due Friday 4/4
  Exercises 6.2: 30, 34, 38, 46, 50, 54.
• Homework 29 - due Monday 4/7
  Exercises 6.3: 4, 8, 10, 12, 16.
• Homework 30 - due Monday 4/14
  Exercises 6.4: 6, 10, 16, 22, 24, 30.
• Homework 31 - due Wednesday 4/16
  Exercises 5.1: 10, 14, 18, 25, 37.
• Homework 32 - due Friday 4/18
  Exercises 5.2: 2, 6, 12.
• Homework 33 - due Monday 4/21
  Exercises 5.2: 16, 20, 23, 28.
• Homework 34 - due Wednesday 4/23
  Exercises 5.2: 26, 30; Exercises 5.3: 6, 8, 11.
• Homework 35 - due Friday 4/25
  Exercises 5.3: 10, 14, 16, 19, 24.
• Homework 36 - due Monday 4/28
  Exercises 5.4: 4, 13, 14, 15.
• Homework 37 - due Wednesday 4/30
  Exercises 5.4: 18, 22 (using both spectral decomposition and orthogonal diagonalization), 25.

Contact Info: Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ 85721. Email: yeap at math.arizona.edu