HOMEWORK 2 SOLUTION
Problem 1(p. 57-15)
(a) If ( A + B)( A B) = AA AB + BA BB = A 2 B 2 , then we have AB + BA = 0 ,
which means that A and B commute in multiplication.
(b) Since A = A , tr ( AB ) = tr ( BA ) = tr ( BA ) ) = tr ( A B ) = tr ( AB ) .
(c) S
HOMEWORK 3
DUE ON 9/30/08
Problem 1 (p. 150-11)
Prove that the only nonsingular idempotent matrices are identity matrices.
Problem 2 (p. 150-14)
For A = cfw_aij explain why
(a) B = A A1(1A1) 1 1A = cfw_aij ai.a. j / a. ;
(b) B has row sums that are zero.
HOMEWORK 1 SOLUTION
Exercise(page 4)
1. set up a vector named u, consisting of 3, 4, 5, 9, 2, 7, 5, 3, 2.
u<-c(3,4,5,9,2,7,5,3,2)
u
[1] 3 4 5 9 2 7 5 3 2
2. set up a vector named v, consisting of 1, 1, 1, 1, 4, 5, 6, 7, 8.
v<-c(1,1,1,1,4,5,6,7,8)
v
[1] 1
HOMEWORK 2
Due on 9/18/2008 before Class
Questions are cited from SR Searle (1982).
Chapter 2
Problem 1 (p. 57-15)
(a) When does (A+B)(A-B) = A 2 -B 2 ?
(b) When A = A , prove that tr ( AB) = tr ( AB) .
(c) When XXGXX = XX , prove that XXG XX = XX .
Probl
Wm
BIOS 6227 Midterm Exam 1 Name: F211! 2008 l
Through the exam, assume that all matrices involved are conformable for the expressions
given.
1. Prove that Trace is invariant to cyclical permutations of matrix multiplication for
the three term case