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Math 136
Sample Term Test 1  2
NOTES:  Questions 7, 10b on this test cover material that will not be covered
on our term test 1.
1.
Short Answer Problems
a) List the 3 elementary row operations.
b) What can you say about the consistency and the number of parameters (free variables)
in the general solution of a system of 5 linear equations in 4 variables.
c) What is the area of the parallelogram induced by
±a
= (1
,

2) and
±
b
= (4
,

9).
d) Let
A
=
±
3
2 1

2 1 4
²
and
B
=

21
11
0

1
. Calculate
AB
.
e) Let
S
=
{
±v
1
,±v
2
3
}
be a set of vectors in
R
3
. State the deFnition of the set
S
being
linearly independent.
f) Explain why
×
(
±
b
×
±
c
) must be a vector in the plane with vector equation
±x
=
s
±
b
+
t±c
,
s, t
∈
R
.
2.
Consider the system of linear equations:

2
x
+3
y
z
=

9
3
x

4
y
+
z
=5

5
x
+7
y
+2
z
=

14
a) Write the augmented matrix and row reduce it to RRE± using elementary
row operations.
b) What is the rank of the coe²cient matrix?
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 Winter '08
 All
 Math

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