Mathematics 317 - Test 2
Date/Time: Friday October 31, 12.10-1.00 in Carver 0060
Material is sections 2.3,2.4, chapters 3, 4 excluding section 4.6,4.7. Questions will be similar to
homework questions (see homework page and model solution).
Keywords are
- Row space, row equivalence (2.3)
- Inverse (2.4)
- Determinants
- ... and row operations (Kitchen Sink Theorem, 3.2)
- ... and invertibility (Kitchen Sink Theorem, 3.3)
- ... and solving linear systems (Kitchen Sink Theorem, 3.3)
- ... and elementary matrices (not in the textbook)
- ... and transposition (3.3)
- Adjoint matrix, Cramer's rule (3.3)
- Eigenvalues, eigenvectors, characteristic polynomial (3.4)
- Vector spaces, subspaces (4.1,4.2)
- Span (4.3)
- Linear independence (4.4)
- Basis, dimension (4.5)
Key methods that you should be comfortable with are
- calculate an inverse by row reducing [A|I]
- Calculating a determinant by row reduction, by 'basketweaving' (down,down,down - up,up,up),
by cofactor expansion and in the simple case that the matrix is triangular (3.2,3.3),
- Calculating an inverse by calculating the adjoint matrix (3.3),
- Calculating the characteristic polynomial of a matrix (3.4),
- Calculating eigenvalues and bases for eigenspaces of a matrix (3.4),
- Checking that a given subset of a vector space is a subspace (4.2),
- Checking given sets of vectors for linear independence
and/or spanning of a vector space (4.3,4.4),
- Calculating bases and dimension for vector spaces (4.5)
Here is a Practice Exam.
Model solutions for practice and real exam have been transferred to WebCT.
Calculators are allowed this time, but will not be necessary.
No laptops, textbooks, notes! You may still bring one help
sheet (double-sided) with theorems, definitions/examples - whatever you
like to have at hand. I recommend to have a watch at hand, even if you do
not normally wear one (but I will announce the time occasionally).