Homework Assignment 8 in MATH309-Spring 2013, c Igor Zelenko
due March 27, 2013 . Show your work in all exercises (you may earn 30 points of bonus)
Sections covered are 6.1, 6.2, and 6.3: Eigenvalues of matrices/linear operators, eigenvectors and
eigenspa
Homework Assignment 9 in MATH309-Spring 2013, c Igor Zelenko
due April 8, 2013 . Show your work in all exercises
Sections covered are 5.1, 5.4.
1. Let x and y be linearly independent vectors in Rn . If |x| = 3 and |y | = 4, what, if anything, can
we concl
Homework Assignment 11 in MATH309-Spring 2013, c Igor Zelenko
due April 24, 2013 . Show your work in all exercises
Topics covered: Elements of Fourier series and their applications in the method of separation of
variables for the heat equation and Laplace
Homework Assignment 10 in MATH309-Spring 2013, c Igor Zelenko
due April 19, 2013 . Show your work in all exercises
Topics covered: Orthonormal sets (section 5.5), boundary value problems for PDEs, classication of
second order linear PDEs, separability and
Bonus Homework Assignment 12 in MATH309-Spring 2013, c Igor Zelenko
Submit it on Friday, May 3 2013 between 10 a.m.-13 p.m. to my oce, Milner 324, or
slide it under my oce door but not later than on the same day, May 3 2013 . Show your
work in all exercis
Homework Assignment 6 in MATH309-Spring 2013, c Igor Zelenko
due March 6, 2013 . Show your work in all exercises.
Sections covered 3.6, 4.1: column/row spaces, rank of the matrix, Rank-Nullity theorem, linear
transformations, kernel and range of a linear
Homework Assignment 7 in MATH309-Spring 2013, c Igor Zelenko
due March 20, 2013 . Show your work in all exercises.
Sections covered 4.2, 4.3 Total of 130 points
1. Assume that a linear transformation L : R3 R2 is given by
L (x1 , x2 , x3 )T = (2x1 3x2 + x
Exam 2, version A
Math 309.501
10/29/14
3
1. A linear transformation
L is dened from P3 (the polynomials of degree less than 3) to R by
p0 (0)
p (1) .
L (p (x) =
p (1)
(a) (10 pts.) Find a basis for the kernel of L. Explainyour answer.(b)
(10 pts.) Find
Homework Assignment 1 in MATH309-Spring 2013, c Igor Zelenko
due January 23, 2013
Please read carefully what you are supposed to nd in each problem.
Sections covered: 1.1, 1.2: consistency/inconsistency, back substitution, augmented matrix of the system,
Homework Assignment 2 in MATH309-Spring 2013, c Igor Zelenko
due January 30, 2013
Sections covered: 1.3, 1.4
1. If
2 1
A = 3 4
6 5
compute
5
2
1 , B = 4
4
2
3
3
1
4
1
3
(a) Compute 3A BA;
(b) AT B T
(c) (BA)T
2. For each of the pairs of matrices A and B t
Homework Assignment 3 in MATH309-Spring 2013, c Igor Zelenko
due February 6, 2013 (you may earn 30 points of bonus). Show your work in all exercises.
Topics covered: Finding inverse both via Jordan-Gauss reduction ( as in section 1.5) and via the
adjoint