## Math 221 Section 204 Lecture Schedule

### Main Page — Quiz/Exam info

Lecture schedule:
 Date Topic Reading to prepare for class Suggested practice problems Lecture Notes Thurs, Jan 4 Linear systems + introduction to row reduction Section 1.1 1.1 exercises 11-14, 15, 17, 19, 23 Scanned Notes Tues, Jan 9 Row reduction, vector equations Sections 1.2+1.3 1.2 exercises 1, 3, 5, 7-11, 13, 15, 17, 21, 23 1.3 exercises 1-4, 7, 11, 17, 23 Scanned Notes Thurs, Jan 11 Vector equations and matrix equations Section 1.4 1.4 exercises 1-4, 9, 10, 11, 12, 21, 22, 23, 24 Scanned Notes Tues, Jan 16 Solution sets of linear systems, starting on applications of linear systems. Sections 1.5-1.6 1.5 exercises 7-10, 13, 14, 15, 23, 24, 26, 27, 28-31, 32, 33 Scanned Notes Thurs, Jan 18 Applications of Linear Systems, starting on linear independence Sections 1.6-1.7 1.6 exercises 1, 3, 7-11, 12-15 (the parts marked with an [M] are intended to be done with a calculator / math software and are optional). Scanned Notes Tues, Jan 23 Linear independence and linear transformations Sections 1.7-1.8 1.7 exercises 1, 2, 5, 7, 9, 10, 15-20, 27, 28, 33-38. (Highlight to check your answers to 34, 36, 38: 34 is false, 36 is false, 38 is true) Scanned Notes Thurs, Jan 25 Linear transformations and their matrices Sections 1.8-1.9 1.8 exercises 3,5,9,11,13-16,18,27,31,32-35 1.9 exercises 1-6,9,10,12,17,19,25,27,28 Scanned Notes Tues, Jan 30 Matrix operations Section 2.1 2.1 exercises 1-4, 9, 10, 12, 13, 18-21, 27 Scanned Notes Thurs, Feb 1 Inverses of matrices Section 2.2 2.2 exercises 1, 3, 5, 6, 8, 12, 21-24, 31, 32, 33 Scanned Notes Tues, Feb 6 Characterizations of invertibility Section 2.3 2.3 exercises 1-8, 13, 17, 21, 23, 27, 33 Scanned Notes Thurs, Feb 8 Midterm 1 Tues, Feb 13 Subspaces of Rn Section 2.5 2.5 exercises 1-4, 7, 9, 11-14, 23, 25, 27-29 Scanned Notes Thurs, Feb 15 Dimension and Rank Section 2.6 2.6 exercises 1, 2, 3, 5, 7, 9, 11, 13, 14 Scanned Notes Tues, Feb 20 No class - midterm break Thurs, Feb 22 No class - midterm break Tues, Feb 27 A bit about coordinates; introduction to determinants Sections 2.6 and 3.1 Scanned Notes Thurs, Mar 1 More on determinants Sections 3.1 and 3.2 3.1 exercises 9, 11, 13, 15-18, 19, 21 3.2 exercises 1-4, 4, 7, 9, 15-20, 21, 25, 29 Scanned Notes Tues, Mar 6 Eigenvectors and eigenvalues Section 4.1 4.1 exercises 1-8, 9, 11, 13, 15, 17-20 Scanned Notes Thurs, Mar 8 The characteristic equation Section 4.2 4.2 exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 18 Scanned Notes Tues, Mar 13 Diagonalization Section 4.3 4.3 exercises 1, 3, 5, 7, 9, 11, 15, 17, 23, 24, 27 Scanned Notes Thurs, Mar 15 Discrete dynamical systems Section 4.6 4.6 exercises 1, 3-7, 15 Scanned Notes Tues, Mar 20 Finishing with eigenvectors, starting inner products Sections 5.1-5.2 5.1 exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 24, 31 Scanned Notes Thurs, Mar 22 Midterm 2 Tues, Mar 27 Orthogonal sets and orthogonal projections Sections 5.2-5.3 5.2 exercises 1, 3, 5, 7, 9, 13, 17 5.3 exercises 1, 3, 5, 11, 13, 15 Scanned Notes Thurs, Mar 29 Orthogonal projections and the Gram-Schmidt process Sections 5.3-5.4 5.4 exercises 1, 3, 5, 7, 9 Scanned Notes Tues, Apr 3 Least-squares problems Section 5.5 5.5 exercises 1, 3, 5, 7, 9, 11, 13, 19, 21 Scanned Notes Thurs, Apr 5 Summary + a few final topics Scanned Notes

Homework schedule:
• WebWork assignment 1: Due Wednesday January 17 (posted Wednesday January 10)
• WebWork assignment 2: Due Wednesday January 24
• WebWork assignment 3: Due Wednesday January 31
• WebWork assignment 4: Due Wednesday February 14
• WebWork assignment 5: Due Wednesday February 28
• WebWork assignment 6: Due Wednesday March 7
• WebWork assignment 7: Due Wednesday March 14
• WebWork assignment 8: Due Wednesday March 28
• WebWork assignment 9: Due Wednesday April 4

The sections listed above are for the textbook for the course, the third custom UBC edition of Linear Algebra and its Applications by David Lay - if you have the non-custom edition the section numbers will be different. For reference, the sections we'll cover in the course are the following.
• 1.1 Systems of linear equations
• 1.2 Row reduction and echelon forms
• 1.3 Vector equations
• 1.4 The matrix equation Ax = b
• 1.5 Solution sets of linear equations
• 1.6 Applications of linear systems (skip economic models)
• 1.7 Linear independence
• 1.8 Introduction to linear transformations
• 1.9 The matrix of a linear transformation
• 2.1 Matrix operations
• 2.2 The inverse of a matrix (skip elementary matrices)
• 2.3 Characterizations of invertible matrices
• 2.5 Subspaces of Rn
• 2.6 Dimension and rank
• 3.1 Introduction to determinants
• 3.2 Properties of determinants
• 4.1 Eigenvectors and eigenvalues
• 4.2 The characteristic equation
• 4.3 Diagonalization
• 4.6 Discrete dynamical systems
• 5.1 Inner product, length, and orthogonality
• 5.2 Orthogonal sets
• 5.3 Orthogonal projections
• 5.3 The Gram-Scmhidt process
• 5.5 Least-square problems