Exam 4 Info
MCS 221 Exam 4 Info
Date & time: Tuesday, December 16, 10:30-12:30
Place: Classroom
Coverage: Determinants, eigenvalues, eigenvectors, and diagonalization
plus comprehensive review:
systems of linear equations, linear independence, spans, dimension,
linear transformations, inner products, and orthogonality
Test 4 will be a closed-book, closed-notes examination.
You may use one new handwritten 3"-by-5" note card.
You may also use your note cards for previous exams.
The problems will be rigged so that you should be able to do the calculations
by hand.
There will not be any Maple problems on the test.
Be prepared for GAC+ problems:
Geometric problems
Algebraic problems
Computational problems
+ a wee bit of proofs.
Be prepared to do problems and use knowledge from the following areas.
- Determinants
- Three equivalent definitions
- By properties
- Explicit formula
- Cofactor expansion
- Row reduction and determinants, the key to practical computation
- Cramer's rule and a formula for the inverse of a matrix
- Eigenvalues, eigenvectors, diagonalization, and matrix representations
- Characteristic polynomials & eigenvalues
- Eigenvectors
- Diagonalization, diagonalizability ("diagonability")
- Orthogonal matrices, orthogonal diagonalization.
- Applications
- Systems of linear equations
- Vector spaces, subspaces
- Linear independence, span, basis, dimension
- Linear transformations, matrix representations
- Linear transformations, fundamental subspaces of
m-by-n real matrices
Fundamental Theorem of Linear Algebra, I
Fundamental Theorem of Linear Algebra, II
- Inner products, orthogonality, Gram-Schmidt process
Last updated 12/12/08.