Math& 208
Linear Algebra
LEARNING OUTCOMES
Upon successful completion of Math& 208, the student
should be able to:
- Solve systems of
linear equations -- small ones manually by row reduction techniques and
larger ones using technology.
- Use linear systems to
model and analyze applied situations.
- Perform matrix
operations, including matrix inversion.
- Translate linear
systems into matrix equations, and use matrix inverses to solve, where
appropriate.
- Perform vector
operations in Rn and interpret them geometrically in R2
and R3.
- Use vectors to solve
"physical" problems.
- Verify and/or refute
the validity of vector space axioms in specific examples.
- Use the vocabulary
of vector spaces (linear combination, span, subspace, linear independence
and linear dependence, basis, dimension, and orthogonal) appropriately in
R2 and R3.
- Apply the vocabulary
of vector spaces (linear combination, span, subspace, linear independence
and linear dependence, basis, dimension, and orthogonal) to specific
examples in Rn.
- Identify and
construct examples of linear combinations, spans, subspaces, linear
independence and linear dependence, bases, dimension, and orthogonality in
spaces of matrices and function spaces.
- Exemplify linear
transformations in R2, R3 and more general settings,
and distinguish linear transformation from non-linear mappings.
- Construct and
analyze matrix representations of linear transformations, and relate them
to matrix operations.
- Describe the effect
(including null space and image) of linear transformations on sets of
vectors, especially in R2 and R3.
- Compute determinants
of 2x2 and 3x3 matrices, and relate them to the geometry of linear
transformations and to the solution of linear systems.