Holy Cross Mathematics and Computer Science
MATH 244, Linear Algebra, Spring 2007
Syllabus and Schedule
Examples, Class Notes, Solutions, Etc.
Assignments
- Guidelines for problem sets
- Problem Set 1: (From Lay)
Section 1.1/30, 32, 33, 34;
Section 1.2/4, 10, 12, 16, 18, 20, 23, 24, 28, 29, 30, 31;
Section 1.3/12, 14, 16, 18, 19, 20, 22, 25.
Due: Friday, January 26.
- Problem Set 2: (From Lay)
Section 1.4/15, 18, 26, 31, 32, 33;
Section 1.5/6, 7, 16, 36, 37, 38;
Section 1.7/1, 6, 9, 32, 34, 36, 38.
Due: Friday, February 2.
- Problem Set 3: (From Lay)
Section 1.8/4, 5, 8, 10, 12, 19, 27, 28;
Section 1.9/2, 4, 6, 8, 31, 32, 35, 36;
Section 2.2/3, 6, 15, 18, 19, 31, 33.
Due: Friday, February 9.
- Discussion 1, writeups Due: Monday, February 12.
- Problem Set 4: (From Lay)
Section 2.3/6, 8, 14, 15, 18, 22, 26, 30, 36, 38;
Section 2.8/8, 16, 18, 26, 32, 34;
Section 2.9/6, 10, 16, 20, 22, 24.
Due: Friday, February 23.
- Problem Set 5: (From Lay)
Section 3.1/2, 10, 22, 24, 34, 36, 38;
Section 3.2/6, 8, 16, 18, 20, 22, 31, 32, 33, 34, 35, 36, 40.
Due: Friday, March 2.
- Problem Set 6: (From Lay)
Section 3.3/4, 6, 8, 20, 24, 29, 30, 32;
Section 4.1/2, 4, 5, 6, 8, 20, 21, 22, 31, 32, 33, 34;
Section 4.2/30, 31, 33, 34.
Due: Friday, March 16.
- Problem Set 7: (From Lay)
Section 4.3/24, 26, 31, 32, 34;
Section 4.4/10, 12, 14, 18, 22, 28;
Section 4.5/26 (Hint: Argue by contradiction -- suppose that H
is strictly contained in V. If x is
a vector that is not contained in H and B is a basis
for H, what can you say about the set B U {x}?), 28, 32.
Due: Friday, March 30.
- Discussion 2 -- writeups Due: Wednesday, April 4.
- Problem Set 8: (From Lay)
Section 4.7/4, 6, 8, 14;
Section 5.4/2, 4, 6 with added part d: Find the matrix of T
relative to the bases {1, t, t2} and
{1, 1 + t, 1 + t + t2, 1 + t + t2 + t3, 1 + t + t2 + t3+
t4}, 8, 10 with added part c: Find the matrix for T
relative to the bases
B = {1 + t2,1 - t, 2, 1 - 3t3} in P3
and C = {e1 + e2, e1 - e2,
e3 + 2e4, e3 - 2e4} for R4;
Section 5.1/2, 6, 8, 20, 24, 25, 26, 36.
Due: Friday, April 13.
- Problem Set 9: (From Lay)
Section 5.2/6, 10, 14, 18, 23, 25;
Section 5.3/12, 14, 24, 26, 32;
Section 6.2/6, 10, 12;
Due: Friday, April 20.
- Discussion 3 -- writeups Due: Monday, April 23.
- Problem Set 10. Due: Wednesday, May 2,
no later than 5:00pm.
Information and Announcements
- Final Exam will be given Thursday, May 10 at 8:30am in SW 359.
- Review session: Monday, May 7 at 5:30pm in SW 359.
- For the final, you should know definitions of:
- reduced row echelon form for matrices
- a linear combination of a set of vectors
- the span of a set of vectors
- linear independence and linear dependence for sets of vectors
- a linear mapping (or linear transformation -- the
terms are synonyms) T : Rn -> Rm
- the inverse A-1 of an n x n matrix A
- a vector subspace of Rn
- the column space Col(A) and null space Nul(A) of a matrix
- a basis for a vector subspace
- the dimension of a vector subspace
- the rank of a matrix (= the dimension of its column space)
- the determinant of an n x n matrix (know how
to write down the expansion by minors (cofactor expansion)
along the ith row for any i, 1 <= i <= n)
- the coordinate vector of x in a vector space
V with respect to a basis B: [x]B.
- the change of coordinates matrix from coordinates with respect
to B to coordinates with respect to B':
PB' <- B. (Note: this is in section 4.7.)
- the eigenvectors and eigenvalues of a linear
transformation T : V -> W or an
n x n matrix A.
- the n x n matrix A is diagonalizable.
- the n x n matrices A,B are similar.
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Last modified: May 11, 2007