Math 551
1.2
Chapter 1: True/False Questions
1. A subset of an independent set is independent.
2. A subset of a dependent set is dependent.
3. If a set of elements of a vector space is dependent, then each element of the set is a
combination of the other
MATH 551 - APPLIED MATRIX THEORY
FINAL TEST: SAMPLE 1 with SOLUTIONS (250 points)
NAME:
PROBLEM 1 (30 points) A web of 5 pages is
given by
01
0 0
A= 1 1
0 0
11
described by a directed graph whose matrix is
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
Do the following (1
MATH 551 - APPLIED MATRIX THEORY
Fall 2006
FIRST SAMPLE OF TEST 2 (Chapters 3, 4, 5, and 6)
PROBLEM 1. Let T : R2 R3 be the linear transformation given by
2x1 + x2
3x1
T (x1 , x2 ) =
4x2
(i) Find a 3 2 matrix A such that T x = Ax for every x = (x1 , x2 )
MATH 551 - APPLIED MATRIX THEORY
Spring 2007
FIRST SAMPLE OF TEST 2 (Chapters 3, 4, and 5)
PROBLEM 1. Let T : R2 R3 be the linear transformation given by
2x1 + x2
3x1
T (x1 , x2 ) =
4x2
(i) Find a 3 2 matrix A such that T x = Ax for every x = (x1 , x2 )
MATH 551 - APPLIED MATRIX THEORY
Fall 2006
FIRST SAMPLE OF TEST 2 (Chapters 3, 4, 5, and 6)
PROBLEM 1. Let T : R2 R3 be the linear transformation given by
2x1 + x2
3x1
T (x1 , x2 ) =
4x2
(i) Find a 3 2 matrix A such that T x = Ax for every x = (x1 , x2 )
Math 551
Exam 2
Name
July 23, 2001
1. Given that the eigenvalues of the matrix A are 2, 1 nd (if possible) a basis
=
1
0 as a linear combination of
of eigenvectors. Is A diagonlizable? Express X =
0
3
eigenvectors and use this to compute A X .
1 1 1
A =
MATH 551
EXAM 1
10:3011:25 pm, Friday
February 24, 2006
Name:
No books or formula sheets are allowed. Use the back page as a sketch paper. For full credit, show
your work in detail.
Total: 100 #1 #2 #3 #4 #5
1 2
1
3
1 (20 pts). Let A =
0
1
1
2
1
2
2 2
NAME
Applied Matrix Theory - MATH 551
Exam 2
November 6, 2000
Show all your work in the space provided under each question. Each problem is worth
10 points.
110
1. Let A = 0 1 0 Find A1 .
011
2. Find a transformation T : R2 R2 which reects points in the y
MATH 551
EXAM 2
10:30-11:20 am, Friday
March 17, 2006
Name:
No books or formula sheets are allowed. Use the back page as a sketch paper. For full credit, show
your work in detail.
Total: 100 #1 #2 #3 #4 #5
1 (20 pts). We have shown that the functions cfw_
From maginnis@math.ksu.edu Fri Dec 19 15:45:01 2003 Date: Fri, 19 Dec 2003 1
From: John Maginnis maginnis@math.ksu.edu To: sheree math@math.ksu.edu Sub
2
Dear Sheree, I think I forgot to give you this second exam.
John Maginnis
Name
Math 551, Applied Matr
Name
Applied Matrix Theory - MATH 551
Final Exam
December 17, 2002
Show all your work in the space provided under each question. Each problem is worth 10 points
except for problem 14 which is worth 20 points.
1
1. Find the coordinates of the vector 1 with
APPLIED MATRIX THEORY
Math 551
Louis Crane - Instructor
Exam I
September 19, 1994
Name
No notes or books!
I. Short answers (5 pts/part)
1. A) Is it possible to multiply
13
25
by
368
427
613
in either order?
B) Why or why not?
2. A) If a system of linear e
Name
Applied Matrix Theory - MATH 551
Exam 1
September 27, 2002
Show all your work in the space provided under each question. each problem is worth 10 points.
1. Find all solutions to the system of equations. (Show your steps.)
x + y 3z = 1
3x y + z = 7
5
Math 551 Exam III Spring 1999 Spring Fever
NAME
1. Let A : R3 R3 ;
40 4
a = 1 2 0 in the standard bases.
-3 0 -4
a) Compute the eigenvalues of A .
b) Compute a maximal set of independent eigenvectors. Is it a basis for R3 ?
2. Find the set of all a , b an
Name
Applied Matrix Theory - MATH 551
Exam 2
November 4, 2002
Show all your work in the space provided under each question. each problem is worth 10 points.
1. Find a transformation T : R2 R2 which rotates points by
radians counterclockwise, ex3
pressing
MATH 551 - APPLIED MATRIX THEORY
Spring 2007
FIRST SAMPLE OF TEST 2 (Chapters 3, 4, and 5)
PROBLEM 1. Let T : R2 R3 be the linear transformation given by
2x1 + x2
3x1
T (x1 , x2 ) =
4x2
(i) Find a 3 2 matrix A such that T x = Ax for every x = (x1 , x2 )
MATH 551 - APPLIED MATRIX THEORY
FINAL TEST: SAMPLE 1 with SOLUTIONS (250 points)
NAME:
PROBLEM 1 (30 points) A web of 5 pages is
given by
01
0 0
A= 1 1
0 0
11
described by a directed graph whose matrix is
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
Do the following (1
MATH 551 - APPLIED MATRIX THEORY
FINAL TEST: SAMPLE 1 (250 points)
NAME:
PROBLEM 1 (30 points) A web of 5 pages is
given by
01
0 0
A= 1 1
0 0
11
described by a directed graph whose matrix is
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
Do the following (10 points each):
MATH 551 - APPLIED MATRIX THEORY
FINAL TEST: SAMPLE 1 (250 points)
NAME:
PROBLEM 1 (30 points) A web of 5 pages is
given by
01
0 0
A= 1 1
0 0
11
described by a directed graph whose matrix is
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
Do the following (10 points each):
Math 551
2.1
Chapter 2: True/False Questions
1. A 5 27 matrix can have six linearly independent columns.
2. I start with a certain 4 6 matrix A and reduce, obtaining
1011 0 0
0 1 1 3 2 3
M =
0 0 0 0 1 1 .
0000 0 0
Which of the following statements abou
Math 551
Chapter 3: True/False Questions
3.1 (1) A linear transformation of R2 into R2 which transforms [1, 2]t to [7, 3]t and [3, 4]t to
[1, 1]t will also transform [5, 8]t to [13, 7]t .
(2) It is impossible for a linear transformation from R2 into R2 to
Math 551
Chapter 6: True/False Questions
6.1 (1) If A is an n n matrix that has zero for an eigenvalue, then A cannot be invertible.
(2) A non-decient 2 2 matrix A has eigenvalues 3 and 0 with [1, 2] t as an eigenvector
corresponding to the eigenvalue = 3
Math 551
Chapter 5: True/False Questions
5.1 (1) The following matrices have the same determinant.
24 2 6
3
3 3 27 33
2
2 1 5 2
6
6 1 3 3
2
639
1 5 2
1 3 3
2 18 22
(2) Let A be a 3 3 matrix. Then det(5A) = 5 det(A).
(3) Let A and B be 3 3 matrices. Th
Math 551
Chapter 4: True/False Questions
4.1 (1) The point [1, 4]t has coordinate vector [1, 2]t with respect to the basis of R2 formed
by the vectors [1, 3]t and [1, 1]t .
(2) There exist ve non-zero, mutually perpendicular vectors X1 , X2 , X3 , X4 , X5