Stephanie Campbell
Assignment 6
MATH133, Fall 2009
due 11/07/2010 at 10:59pm EST.
You may attempt any problem an unlimited number of times.
1.
(1 pt) Solve the system using elimination
2
x

7
y
=

49

5
x
+
7
y
=
28
x
=
y
=
2.
(1 pt) Write the system

2
y

7
z
=
11
2
x
+
9
y
=

4

6
x
+
10
y
+
4
z
=
3
in matrix form.
x
y
z
=
3.
(1 pt) Given the augmented matrix
A
, perform each row
operation in order, (a) followed by (b) followed by (c).
A
=
1
1
1
5
3
2
5
5
4
0
4
6
(
a
)
R
2
=

3
r
1
+
r
2
(
b
)
R
3
=
4
r
1
+
r
3
(
c
)
R
3
=
4
r
2
+
r
3
4.
(1 pt) Reduce the matrix
1
3
2
24
4
3
0
28
2
2
1
20
to reduced
rowechelon form.
5.
(1 pt) Find the ranks of the following matrices.
rank
0
2
0
1
0
9
=
rank
4
5
4
5
=
rank
5
1
5
0
2
0
4
0
4
=
6.
(1 pt) Find the determinant of the matrix
B
=
4
5
4
2
5
3
3
4
5
.
det
(
B
) =
.
7.
(1 pt) Find the determinant of the matrix
A
=
2
0
0
0
7
5
0
0
5
4
2
0
1
3
8
2
.
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 Fall '08
 KLEMES
 Math, Linear Algebra, Matrices, Characteristic polynomial, Eigenvalue algorithm, Let Kunovice

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