Chabot College
Fall 2010
Course Outline for Mathematics 6
ELEMENTARY LINEAR ALGEBRA
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Catalog Description:
MTH 6 - Elementary Linear Algebra
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3.00 units
Introduction to linear algebra: matrices, determinants, systems of equations, vector spaces, linear
transformations, eigenvalue, eigenvectors, applications.
Prerequisite: MTH 2 (completed with a grade of "C" or higher)
Units
Contact Hours
Week
Term
3.00
Lecture
Laboratory
Clinical
Total
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3.00
3.00
0
0.00
3.00
52.50
0
0.00
52.50
Prerequisite Skills:
Before entry into this course, the student should be able to:
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define natural logarithmic function in terms of a Riemann integral;
integrate and differentiate logarithmic functions;
define and differentiate inverse functions;
define an exponential function;
differentiate and integrate exponential functions;
differentiate and integrate inverse trigonometric functions;
differentiate and integrate hyperbolic functions and their inverses;
solve application problems involving logarithmic, exponential, inverse trigonometric, and hyperbolic
functions;
solve differential equations using separation of variables;
use standard techniques of integration such as integration by parts, trigonometric integrals,
trigonometric substitution, partial fractions, rational functions of sine and cosine;
graph polar equations and find area of regions enclosed by the graphs of polar equations;
evaluate limits using L’Hopital’s Rule;
evaluate improper integrals;
use parametric representations of plane curves;
perform basic vector algebra in R^2 and R^3 and interpret the results geometrically;
find equations of lines and planes in R^3;
construct polynomial approximations (Taylor polynomials) for various functions and estimate their
accuracy using an appropriate form of the remainder term in Taylor’s formula;
determine convergence of sequences:
determine whether a series converges absolutely, converges conditionally or diverges;
construct (directly or indirectly) power series representations (Taylor series) for various functions,
determine their radii of convergence, and use them to approximate function values.
Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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solve systems of linear equations using Gaussian elimination, matrix, and determinant techniques;
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Course Content:
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Solution of systems of linear equations by various techniques
The algebra of matrices; inverses, transposes, determinants
Vector spaces, subspaces, linear independence, bases, dimension, row and column space, inner
product spaces, orthonormal bases, Gram-Schmidt Process
Linear transformations, their properties and matrix representations, geometry of linear
transformation, change of basis
Eigenvalue problems, similarity, orthogonal bases, and diagonalizing matrices
Applications: quadratic forms, the Principal Axes Theorem, approximation, Fourier series (if time
permits)
Methods of Presentation
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compute determinants of all orders;
perform all algebraic operations on matrices and be able to construct their inverses, adjoints,
transposes; determine the rank of a matrix and relate this to systems of equations;
recognize and use the properties of vector spaces and inner product spaces, and understand the
concepts of subspaces, linear independence, bases, orthogonality, and their relation;
identify and use the properties of linear transformations and their relation to matrices;
solve eigenvalue problems, diagonalize and orthogonally diagonalize matrices.
Lecture/Discussion
Demonstration/Exercise
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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Find the standard matrix for the stated composition of linear operators on R^2. 1) A
rotation of 90 degrees, followed by a reflection about the line y = x. 2) An orthogonal
projection on the y-axis, followed by a contraction with factor k = 0.5. 3) A reflection about
the x-axis, followed by a dilation with factor k = 3.
Let V be an inner product space. Show that if w is orthogonal to both u1 and u2, it is
orthogonal to k1u1 + k2u2 for all scalars k1 and k2. Interpret this result geometrically in
the case where V is R3 with the Euclidean inner product.
2. Methods of Evaluating Student Progress
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Textbook (Typical):
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Exams/Tests
Quizzes
Home Work
Howard Anton (2009). Elementary Linear Algebra Wiley Publishing.
Special Student Materials
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A calculator may be required.