ASSIGNMENT 1 EE441 KUMAR Fall 2007 Due: Sep. 7 1. Qn 2 from Question Bank (on Blackboard) 2. Problem set 1.4 of the textbook, questions: 2,6,11,14,19. These are reproduced below: 2. Working a column at a time, compute the products:
4 1 5 1 6
ASSIGNMENT 2 EE441 KUMAR Fall 2007 Due: Sep. 14 1. "A typical Chinese problem, taken from the Han dynasty text Nine Chapters of the Mathematical Art (about 200 B.C.) reads: There are three classes of corn, of which three bundles of the first class, t
ASSIGNMENT 3 EE441 KUMAR Fall 2007 Due: Sep. 21 1. Factor the symmetric matrix A = 13 10 10 8 .
into a product A = SS T (Cholesky decomposition), where S is a lower triangular matrix. 2. Is the matrix
A=
1 -2 1 0 6 -3 16 -4 2 4 7 -2 3 -6 6 2
ASSIGNMENT 4 EE441 KUMAR Fall 2007 Due: Oct. 1 (Monday, please note) 1. Identify geometrically, as clearly as you can, the subset of 3-dimensional (Euclidean) space 3 that corresponds to the column space of the matrix 0 2 A = 3 5 . 4 0 2. Let S be
ASSIGNMENT 5 EE441 KUMAR Fall 2007 Due: Monday, Oct. 8 1. How many possible patterns can you find (like the (5 8) example matrix U in Fig. 2.3 , page 79 of the text) for (2 3) row-reduced echelon matrices. Entries to the right of the pivots are irr
ASSIGNMENT 6 EE441 KUMAR Fall 2007 Due: Monday, Oct. 15 1. Find a basis each for the rowspace, columnspace and nullspace of the matrix
A =
1 1 2 3
2 3 5 6
0 -1 1 1 . 1 0 0 0
2. What is the coordinate representation of the vector [1 0
ASSIGNMENT 7 EE441 KUMAR Fall 2007 Due: Monday, Nov. 5 1. The nullspace of a certain (3 3) matrix is a plane in origin. What is the rank of A ?
3
that passes through the
2. The (4 3) matrix A has rank 3. Which of the following is true of A ? (a)