FIRST EXAMA
Instructions:
Begin each of the eight numbered problems on a new page in your answer book.
Show your work, and
mention theorems when appropriate
.
1.
[15 Pts] Find the general solution of the following homogeneous system of equations. Express your answer using vector
notation. Use the method developed in class. What is an appropriate (mental) geometric picture for this solution set?
±
x
1
−
3
x
2
−
9
x
3
+5
x
4
=0
x
2
+2
x
3
−
x
4
2.
[15] Determine which of the following sets of vectors are linearly independent. Give reasons for your answers.
a.
⎡
⎣
10
−
6
2
⎤
⎦
,
⎡
⎣
5
−
3
1
⎤
⎦
b.
⎡
⎣
1
−
2
−
1
⎤
⎦
,
⎡
⎣
0
0
0
⎤
⎦
,
⎡
⎣
3
−
5
−
4
⎤
⎦
c.
⎡
⎢
⎢
⎣
1
1
0
−
1
⎤
⎥
⎥
⎦
,
⎡
⎢
⎢
⎣
−
2
1
−
3
5
⎤
⎥
⎥
⎦
,
⎡
⎢
⎢
⎣
1
−
1
2
−
3
⎤
⎥
⎥
⎦
,
⎡
⎢
⎢
⎣
0
9
−
4
4
⎤
⎥
⎥
⎦
3.
[15] Let
A
=
⎡
⎣
11
−
2
−
1
−
1
−
3
⎤
⎦
,
y
=
⎡
⎣
2
−
7
4
⎤
⎦
, and de±ne
T
:
R
2
→
R
3
by
T
(
x
)=
A
x
.
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This note was uploaded on 04/08/2012 for the course MATH 340 taught by Professor Davidglenn during the Spring '12 term at Boston Architectural.
 Spring '12
 DavidGlenn
 Algebra, Equations

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