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Final Exam, Math 20F
Signature
July 31, 1998
Section #
Name
(Print, with noneraseable pen)
This exam is closed book, closed notes and closed calculator. Please work alone, and show
and explain your work and justify your answers–give clear explanation in plain language
combined with suitable equations. Each problem is worth 55 points for a total of 10
×
55=550 points.
1. Let
230100
010200
000100
0000
cd
be the echelon form of the augmented matrix of the system
Ax
=
b
, with
A
a4
×
5
matrix.
Given the general solution in the 3 cases:
c
6
=0
6
=
d
;
c
6
=0=
d
; and
c
6
=
d
.
2. For
A
=
123
01

1
0

11
give a basis of Null(
A
) and a basis of Col(
A
).
3. Find the general solution of the system
2
x
1
+3
x
2
+11
x
3
+6
x
4
=11
x
2
x
3
+5
x
4
=6
x
1
+
x
2
+2
x
3
=1
.
4. Find the inverse
A

1
of
A
=
1

21
4

77

36

2
.
5. Find a basis of the vector space spanned by the 4 vectors.
1
0
0
1
,
1

1
1

2
,

1
2

1
6
,

4
3

3
5
.
6. Compute the determinant of
A
=
121 1

131

1

112 3

111

1
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 Spring '03
 BUSS
 Math

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