Math 570A Midterm Fall 2009
Name Show your work and write neatly Only write on one side of the paper Number your pages and put your name on each page Avoid writing too close to the corners of the page 1) Let 11 1 0 01
1 1 A= 1
Answer yes or no to the foll
Assignment 4 Math 570A Fall 2009 1) Let A, B Cnn . Recall (A) is the set of eigenvalues of A. Show that (AB ) = (BA). 2) For the matrix A= 1 2 3 2
nd a matrix X such that X 1 AX is diagonal with the eigenvalues of A on the diagonal (see example 7.1.4) 3)
Homework 3 Math 570A Fall 2009
Do the following problems from the book 2.7.2, 3.1.1, 3.2.4
1) For the matrix
2 1 1 3 0 0 2 0 A= 4 1 2 6 6 1 2 3
nd the LU -decomposition and use forward and back substitution to solve 13 2 Ax = 24 14
2) Let C Rnn and b R