Princeton University
Department of Mathematics
MAT 202 – Linear Algebra with Applications
MIDTERM – March 14, 2007
•
You have
1 hour and 30 minutes
to complete your work.
•
Please
show all work
, explain your answers and write neatly.
•
Each lettered part of a problem corresponds to 5 points.
•
Books, notes, calculators, computers are not permitted on this exam.
•
The average on this exam was 69%.
(1) Let
A
=
1
0
1
4
2
3
4
4
0
1
6
4
.
(a) Find the reduced rowechelon form of
A
.
(b) Determine all solutions of
Ax
= 0
.
(c) Determine all solutions of
Ax
=
b
where the vector
b
is the sum of the first two columns of
A
.
(2) Consider the matrix
A
=
1
0
2
0
1
1
2
1
5
.
(a) Find a basis of the image of
A
.
(b) Compute the coordinates of
3

1
5
in the basis you found in (a).
(c) Find a basis for
(
im
A
)
⊥
, the orthogonal complement of the image of
A
.
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2
(3) Let
V
be the subspace of
R
4
with basis
v
1
=
1
0
0
0
,
v
2
=
1
1
0
1
and
v
3
=
1
0
1
1
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 Spring '08
 Staff
 Linear Algebra, Algebra, Orthonormal basis

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