July 26, 2005
PRELIM 3
Math 294 (50 minutes)
Do questions 1-3 and one of 4 and 5. If you do both, only question 4 will count
towards your grade.
Show your reasoning and all your work. Calculators are not needed or permitted.
Good luck!
Problem 1 (25 point
Prelim 1
Math 294
Summer 2005
Tuesday June 28, 50 minutes
Show your reasoning and all your work. Calculators are not needed or permitted.
Good luck!
Problem 1 (25 points). Find all solutions of the system of equations
x1
+
x2
2x3
+
+
x4 +
2x5
x5
x5
=
=
=
July 13, 2012
Prelim 1
Math 2940
Please show your reasoning and (except on question 6) all your
work. This is a 75 minute exam. Calculators are not needed or permitted.
Good luck!
Problem 1) (10 Points) Find the
0
0
1
Problem 2) (10 Points)
required so th
July 12, 2005
PRELIM 2
Math 294 (50 minutes)
Show your reasoning and all your work. Calculators are not needed or permitted.
Good luck!
Problem 1 (20 points)
For the matrix C given by
1
1
C=
1
1
its reduced row echelon form (rref) A
1
0
A=
0
0
1
1
1
1
2
July 26, 2012
Prelim 2
Math 2940
Please show your reasoning and (except on question 7) all your
work. This is a 75 minute exam. Calculators are not needed or permitted.
Good luck!
Problem 1) (15 Points) Find the special solutions of x1 + 3x2 4x3 = 0
and u
Math 2940, Prelim 2, October 25, 2012
This is a closed book prelim. Calculators are NOT allowed. SHOW ALL WORK!
123
1) Let A = 1 2 3 .
123
a) (8 points) What is det(A)?
b) (8 points) Find all eigenvalues and eigenvectors of A.
2) For the questions below,
Math 2940, Final Exam, December 12, 2011
You are NOT allowed calculators or the text. With the exception of True/False questions, JUSTIFY ALL
ANSWERS, SHOW ALL WORK!
1) (14 points) Find the solution to the given system of dierential equations, satisfying
Math 2940, Prelim 2
October 27, 2011
You are NOT allowed calculators or the text. With the exception of True/False questions,
JUSTIFY ALL ANSWERS, SHOW ALL WORK!
1) (a) (10 points) Find a basis for the subspace of all vectors in R4 orthogonal to both
(1,
Math 2940, Prelim 2 Solutions, October 25, 2012
123
1) Let A = 1 2 3 .
123
a) (8 points) What is det(A)?
Solution: The rows are dependent so the matrix is NOT invertible. Hence its determinant
is 0.
b) (8 points) Find all eigenvalues and eigenvectors of A
Math 2940, Prelim 1
September 27, 2012
This is a closed book prelim. Calculators are NOT allowed. SHOW ALL WORK!
1) a) (7 points) Find all solutions to
a + 2b + 3c + 4d = 10, 2a + 4b + 6c + 9d = 24, 3a + 6b + 8c + 14d = 36.
3
6
9
b) (7 points) Let v1 = h
Math 2940, Prelim 1
September 29, 2011
You are NOT allowed calculators or the text. SHOW ALL WORK!
10
2
1) A matrix A was reduced to A = 0 1 1 by the following row operations in the
00
0
given order:
2 times Row 1 subtracted from Row 2, 4 times Row 1 adde
Math 2940, Prelim 2
October 27, 2011
You are NOT allowed calculators or the text. With the exception of True/False questions,
JUSTIFY ALL ANSWERS, SHOW ALL WORK!
1) (a) (10 points) Find a basis for the subspace of all vectors in R4 orthogonal to both
(1,