MAS 3105
AM: March 13, 2008
Quiz 5
Prof. S. Hudson
1) Answer TRUE or FALSE: [the ‘
A
’ in part b) is
not
the same as in c), and so on]
a) Two row equivalent matrices must have the same rank and the same nullity.
b)
A
x
=
b
is consistent if and only if
b
is in the column space of
A
.
c) If
A
is a transition matrix, then
A
is square and det
A
= 0
d) The rank of
A
is greater than or equal to the number of columns of
A
.
e) If
A
represents
L
:
R
3
→
R
2
then
A
is a 2x3 matrix.
2) These two matrices are row equivalent:
A
=
1
2
0
3
0
1
2
1
3
1
2
4
0
6
7
and
U
=
1
2
0
3
0
0
0
1
0
0
0
0
0
0
1
.
a) Find a basis of the row space of
A
.
b) Find a basis for the column space of
A
.
c) Find a basis for the nullspace of
A
.
d) Find the rank of
A
.
e) Find the nullity of
A
.
3) Choose ONE of these.
A) Let
L
be the operator on
P
3
defined by
L
(
p
(
x
)) =
xp
(
x
) +
p
(1). Find the matrix
A
representing
L
with respect to [1
, x, x
2
].
B) State and prove Theorem 5.1.1, the formula for the dot product which includes
θ
.
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Matrices, column space, row equivalent matrices, Prof. S. Hudson

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