Math 22A
UC Davis, Winter 2011
Prof. Dan Romik
Final exam notes
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Final exam date, time and place: March 16, Young Hall 198 at 3:30 PM.
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Exam duration: 2 hours.
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Exam type: closed book exam — no written material or electronic devices
allowed.
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Exam material: the exam will cover all the material covered in class, with a
greater emphasis on material covered after the second midterm.
Practice questions for the ﬁnal
1.
You are given the linear system of equations
2
x
1
+ 4
x
2
+
x
3
+
x
4
=
8
x
1
+ 2
x
2
+
x
3
=
5

x
1

2
x
2
+
x
3

2
x
4
=

1
x
1
+ 2
x
2
+
x
4
=
3
(a) Write an augmented matrix representing the system.
(b) Find a reduced row echelon form (RREF) matrix that is rowequivalent
to the augmented matrix.
(c) Find the general solution of the system. It should be expressed in the
form
{
X
0
+
λ
1
Y
1
+
λ
2
Y
2
+
...
+
λ
k
Y
k
}
where
X
0
,Y
1
,...,Y
k
are some vectors in
R
4
and
λ
1
,...,λ
k
are free pa
rameters.
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 Winter '08
 chuchel
 Math, Linear Algebra, Algebra, augmented matrix, Final exam date, adjoint matrix adj

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