MATH 3000 (Azoff)
Linear Algebra
Fall 2009
Last updated December 18.
Grades have been reported to the registrar. The median on the final exam was 153 out
of 200.
Exams are available for pick-up.
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MATH 3000 EXAM 1 PRACTICE SHEET
Computation
(1) Write the general solution to the following system of equations in parametric vector
notation (for example x = a + tb + sc, for some vectors a, b, c):
x2 + 2 x3 = 1
x1 + 4 x2 + 8 x2 = 6
3x1 + 2x2 + 4x3 = 8
(
Math 3000, Fall 2011, Practice Sheet for Exam 3
1.
Let A =
13
. Find A1 .
0 1
2.
Suppose A and B are n n matrices. Prove that the following two statements are
equivalent
a. det(A B ) = 0
b. there exit nonzero vectors v such that Av = Bv
3.
Let V < R4 be t
MATH 3000, FALL 2011
INSTRUCTOR: DANIEL KRASHEN
Basic
Course Information
Lectures: MWF 10:10-11:00, Boyd 222
Oce Hours: Wednesdays 11:00-12:00, Boyd 437 or by appointment
Oce Phone: 542-2555
Email: dkrashen@math.uga.edu
Textbook: Linear Algebra: A Geometr
MATH 3000 (Azoff) Fall 2009
Study Guide for Third Hour Test (Section 3.6 and Chapters
4, 5, and 6)
Section 3.6:
Abstract Vector Spaces (up through Example 9, i.e., not
responsible for inner products)
Definition and subspaces
Examples: spaces of matrices a
MATH 3000 (Azoff) Fall 2009
Study Guide for Chapters 1 and 2 (First Hour Test)
Definitions
Rn
unit vector
line in Rn (parametric form)
hyperplane in Rn (cartesian or normal form)
linear combination of vectors
dot product of vectors
orthogonal (or perpendi
MATH 3000 (Azoff) Fall 2009
Study Guide for Chapters 1 and 2
Definitions
Rn
unit vector
line in Rn (parametric form)
hyperplane in Rn (cartesian or normal form)
linear combination of vectors
dot product of vectors
orthogonal (or perpendicular) vectors
ang
MATH 3000 (Azo)
Fall 2009
Practice First Exam with Answers (100 points)
1 (16 points). Find the general solution to the following system of three equations
in four unknowns.
x1 + 3 x 2 x 3 3 x 4 = 0
2 x1 + 6 x2 x3 4 x 4 = 1
x1 3x2 + 2x3 + 4x4 = 2
Answer:
MATH 3000 (Azo)
Fall 2009
Practice First Hour Exam (100 points)
1 (16 points). Find the general solution to the following system of three equations
in four unknowns.
x1 + 3 x 2 x 3 3 x 4 = 0
2 x1 + 6 x2 x3 4 x 4 = 1
x1 3x2 + 2x3 + 4x4 = 2
2 (7 points). Co
MATH 3000 (Azo)
Fall 2009
Notes to Problems from Section 3.6
3.6.2. (Parts a), c), and e) were assigned.) Decide which sets of vectors are linearly independent.
10
01
11
a) The set of two-by two matrices consisting of A :=
, B :=
, C :=
01
10
1 1
These ar