Linear Algebra
Mathematics 124 B Spring 2007
Problem Assignment # 3
Due Monday,March 5
1) Section 3.2: 36, 40, 43, 46
2) Section 3.3: 15, 23, 28, 29
3) Suppose that T:
R
n
๎
R
m
is a linear transformation and that
v
1
,
v
2
,
๎
๎
๎
,
v
p
are vectors in
R
n
.
(a) If S = {
v
1
,
v
2
,
๎
๎
๎
,
v
p
} is linearly independent in
R
n
, does it follow that
W = {T
๎
v
1
๎
,
T
๎
v
2
๎
,
๎
๎
๎
,
T
๎
v
p
๎
} is linearly independent in
R
m
?
Justify your answer with either a proof or a counterexample.
(b) If W = {T
๎
v
1
๎
,T
๎
v
2
๎
,
๎
๎
๎
,T
๎
v
p
๎
} is linearly independent in
R
m
, does it follow that
S = {
v
1
,
v
2
,
๎
๎
๎
,
v
p
} is linearly independent in
R
n
?
Justify your answer with either a proof or a counterexample.
m124bhw3.nb
1