STA 6246 Linear Models
Fall 2011
Homework #1
Due Friday September 9
1 Suppose A and B are n n matrices. Prove from rst principles, i.e. using the denition
of a nonsingular matrix (see page 19 of the notes), that if either AB or BA is nonsingular,
then bot
STA 6246 Linear Models
Fall 2011
Homework #2
Due Friday September 23
1 Let W be the subspace of R3 spanned by x1 = (2, 1, 0) and x2 = (0, 1, 1) . Calculate the
matrix that gives the orthogonal projection onto W .
2 Let be an orthogonal n n matrix. Show th
Masters Program
Fall 1
Regression
(STA 6207)
Spring 1
Design
(STA 6208)
Theory I
(STA 6326)
Theory II
(STA 6327)
Matrix/Computing
(STA 6329)
Elective
Summer 1
Spring 2
Elective
Elective
FYE
Fall 2
Linear Models
(STA 6246)
Elective
Elective
Elective
36 tot
STA 6326
CHAPTER 1 - SOLUTIONS
Problem 1.3
(c) Formally,
( A B)
c
= cfw_ x S : x A B
and
Ac B c = cfw_ x S : x A and x B .
Let x ( A B ) . Since x A B then x A and x B . Therefore, x Ac and
c
(
)
(
)
c
c
c
c
x B c . Hence, x A B . Consequently, ( A B ) A