MA 405 - Linear Algebra and Matrices - Section 001 - Spring 2010 Meeting at: SAS 2235 on M/W/F from 910 - 1000

Office Hours (Spring 2010)

1030 - 1145 M/W, and by appointment.
3143 MSB (SAS Hall)

Announcements

• (12 Jan) Welcome back! I highly recommend bookmarking this page. It will be frequently referred to.

• (5 Feb) Exam 1 will cover sections 1.1 - 1.6.

References and Resources

• Course syllabus can be found here.

• Self Assessment Quizzes provided by the book's publisher

Exercises and Assessments

Section	-
1.2	page 23: Q3, 6, 10, 11, 15, 17, 20, 21-28, 31, 33, 41, 43, 47
QUIZ 1	[original] / [solutions]
1.3	page 37: Q5, 9, 10, 11, 19, 23, 25, 31, 35, 42, 43, 44
QUIZ 2	[original] / [solutions]
1.4	page 45: Q5, 7, 13, 17, 21, 27, 29, 31, 33, 35
1.5	page 51: Q5, 9, 13, 15, 17, 19, 25, 29
QUIZ 3	[original] / [solutions]
1.6	page 65: Q 1-4, 9, 10, 11, 15, 18, 19, 27-30, 35, 38, 52
Exam 1 Study Guide	[link] / solutions: [P1] [P2] [P3] [P4]
Extra Credit 1	[original] / [(X) solutions]
Midterm Exam 1	[original] / [solutions]
1.7	page 77: Q 1-4, 5, 7, 8, 12-14, 18, 19, 23, 27, 30-32
3.1	page 137: Q 2, 3, 7, 8, 11, 12, 13, 14-19, 22, 26, 27
QUIZ 4	[original] / [solutions]
3.2	page 154: Q 5-10, 12, 13, 19, 23, 25, 26, 27, 29, 32, 37-40, 41, 42, 43, 45, 47, 48, 50
QUIZ 5	[original] / [solutions]
3.3	page 171: Q 1, 2, 4, 5, 6, 9, 11, 12, 13, 17, 19, 20, 24, 26, 38, 39, 41
QUIZ 6	[original] / [solutions]
Exam 2 Study Guide	[link]
3.4	page 182: Q 1-8
Midterm Exam 2	[original] / [solutions]
4.1	page 211: Q 1, 3, 5, 9, 11, 13, 15, 19, 23, 24, 26, 27, 44
Extra Credit 2	[original] / [(X) solutions]
QUIZ 7	[solutions]
4.2	page 223: Q 1, 5, 9, 13, 17, 19, 25, 2731, 33, 34, 39
4.4	page 245: Q1, 3, 4, 5
QUIZ 8	[solutions]
5.1	page page 285: Q1, 3, 7, 11, 13, 16, 18, 19, 22, 25, 29, 30
5.2	page 298: Q3, 7, 11, 21, 23, 27, 28, 29, 30, 31, 32, 33
6.1	page 332: Q29, 30, 34, 36
6.2	page 341: Q3, 8, 9, 10, 11, 12, 27, 29, 30, 33
QUIZ 9	[original] / [solutions]
6.3	page 353: Q3, 5, 11, 13, 15, 17, 21, 28, 29, 30, 32, 33
6.4	page 364: Q5, 7, 13, 16, 17, 23, 25, 27
Exam 3 Study Guide	[link] / [solutions]
Midterm Exam 3	[original] / [solutions]
6.6	page 383: Q7, 10, 13, 15, 16, 22, 23, 24, 25, 26, 27, 29
Extra Credit 3	[original] / [(X) solutions]
Final Exam Study Guide	[link] / [solutions]
Final Exam	[link] / [solutions]

Tentative Schedule

# Lectures	Sections	Topics
3	1.1, 1.2	Linear systems of equations, elementary row operations, row echelon form of a matrix, Gaussian elimination
3-5	1.3 - 1.5	Matrix algebra: definition of a matrix, operations with matrices and their properties, invertible matrices, inverse of a matrix. Matrix equations
3-5	1.6, 1.7	Determinants and their properties; applications of determinants: finding the inverse of a matrix, Cramer's Rule. Elementary matrices and LU decomposition
1		Exam 1 Friday, 12 February
4-5	3.1, 3.2	Vector spaces: axioms, subspaces, spanning sets, linear independence of vectors.
4-5	3.4, 3.5	Basis and dimension of vector spaces, coordinate matrix, fundamental subspaces associated with a matrix, the relationship between the rank and nullity of a matrix
3-4	4.1 - 4.3	Linear transformations: definition, examples, matrix representation of linear transformations between Euclidean vector spaces, similarity between square matrices.
1		Exam 2 Friday, 12 March
4-5	5.1 - 5.3	Eigenvectors and eigenvalues, diagonalization of a matrix, symmetric matrices, applications
4-5	6.5, 6.6	Least Squares Approximation. Diagonalization of real symmetric matrices by orthogonal matrices
1		Exam 3 Friday, 23 April
1-2	6.8	Singular Value Decomposition of Matrices
		Final Exam Monday, 10 May 8am - 11am