Fall 2014

Time and venue:  MWF 10:20–11:10 a.m., BLOC 160

First day hand-out

Office hours (BLOC 223b):
Help sessions (BLOC 117):
Additional office hours (BLOC 223b):


Homework assignments ##1-11



Quiz 1:  Wednesday, December 3  (solution)
Quiz 2:  Friday, December 5  (solution)


Final exam:  Tuesday, December 16, 8:00-10:00 a.m., BLOC 160

Rules for the test:  no books, no lecture notes, no computing devices.  Bring paper and a stapler.

Sample problems for the final exam (Solutions)

Sample problems for Test 1 (Solutions)

Sample problems for Test 2 (Solutions)



Course outline:

Part I: Elementary linear algebra


Leon's book: Chapters 1-2


Lecture 1: Systems of linear equations.
Lecture 2: Gaussian elimination.
Lecture 3: Row echelon form. Gauss-Jordan reduction.
Lecture 4: System with a parameter. Applications of systems of linear equations.
Lecture 5: Matrix algebra.
Lecture 6: Diagonal matrices. Inverse matrix.
Lecture 7: Inverse matrix (continued).
Lecture 8: Elementary matrices. Transpose of a matrix. Determinants.
Lecture 9: Properties of determinants.
Lecture 10: Evaluation of determinants. Cramer's rule.

Part II: Abstract linear algebra


Leon's book: Chapters 3-4


Lecture 11: Vector spaces.
Lecture 12: Subspaces of vector spaces.
Lecture 13: Span. Spanning set.
Lecture 14: Linear independence.
Lecture 15: Wronskian. The Vandermonde determinant. Basis of a vector space.
Lecture 16: Basis and dimension.
Lecture 17: Basis and dimension (continued). Rank of a matrix.
Lecture 18: Nullity of a matrix. Basis and coordinates. Change of coordinates.
Lecture 19: Review for Test 1.
Lecture 20: Change of coordinates (continued). Linear transformations.
Lecture 21: Properties of linear transformations. Range and kernel. General linear equations.
Lecture 22: General linear equations (continued). Matrix transformations. Matrix of a linear transformation.
Lecture 23: Matrix of a linear transformation (continued). Similar matrices.

Part III: Advanced linear algebra


Leon's book: Sections 5.1-5.6, 6.1, 6.3


Lecture 24: Euclidean structure in Rn.
Lecture 25: Orthogonal complement. Orthogonal projection.
Lecture 26: Orthogonal projection (continued). Least squares problems.
Lecture 27: Norms and inner products.
Lecture 28: Inner product spaces. Orthogonal sets.
Lecture 29: Orthogonal bases. The Gram-Schmidt orthogonalization process.
Lecture 30: The Gram-Schmidt process (continued). Eigenvalues and eigenvectors.
Lecture 31: Eigenvalues and eigenvectors (continued). Characteristic equation.
Lecture 32: Eigenvalues and eigenvectors of a linear operator.
Lecture 33: Basis of eigenvectors. Diagonalization.
Lecture 34: Review for Test 2.

Part IV: Topics in applied linear algebra


Leon's book: Sections 5.5, 5.7, 6.1-6.4


Lecture 35: Matrix polynomials. Matrix exponentials.
Lecture 36: Complex eigenvalues and eigenvectors. Symmetric and orthogonal matrices.
Lecture 37: Orthogonal matrices (continued). Rigid motions. Rotations in space.
Lecture 38: Orthogonal polynomials.
Lecture 39: Markov chains.
Lecture 40: Review for the final exam.