This preview shows page 1. Sign up to view the full content.
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
.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '12
 DavidGlenn
 Algebra, Equations

Click to edit the document details