In-class Exam I, MATH304/506, 09/18/2012
Instructions please read these carefully rst!
(1) Please write your answers in a blue book. Do not forget to write your
name on the blue book. If you do not ha
Math 304 Section 503 Exam 1 a Jean Marie Linhart Spring 2011
An Aggie does not lie, cheat, or steal or tolerate those who do
On my honor as an Aggie, I have neither given nor received unauthorized ai
MATH 304505 Sample problems for the final exam
Spring 2011
Any problem may be altered or replaced by a different one!
Problem 1 (15 pts.) Find a quadratic polynomial p(x) such that p(-1) = p(3) = 6 an
Chapter3.5
Problem 1E
For each of the following, find the transition matrix
corresponding to the change of basis from cfw_u 1 , u 2 to cfw_e 1 ,
e 2 :
(a) u 1 = (1, 1) T , u 2 = (1, 1) T
(b) u 1 = (1
Chapter7.2
Problem 1E
Let
Factor A into a product LU, where L is lower triangular
with 1s along the diagonal and U is upper triangular.
Step-by-step solution
step 1 of 4
step 2 of 4
step 3 of 4
step 4
In-class Exam 3, MATH304/507, 04/23/2015
Solutions Summary
For some questions, I have given only a summary of the solution,
whereas you were required to show full working in order to get full
credit.
In-class Exam 3, MATH304/507, 04/23/2015
Instructions please read these carefully first!
(1) Please write your answers in a blue book. Do not forget to write your
name on the blue book. When you have
Chapter2.3
Problem 1CTA
For each of the statements that follow, answer true if the
statement is always true and false otherwise. In the case
of a true statement, explain or prove your answer. In the
c
Chapter7.6
Problem 1E
Let
(a) Apply one iteration of the power method to A, with any
nonzero starting vector.
(b) Apply one iteration of the QR algorithm to A.
(c) Determine the exact eigenvalues of A
Chapter5.2
Problem 1E
For each of the following matrices, determine a basis for
each of the subspaces R(A T ), N(A), R(A), and N(A T ):
Step-by-step solution
step 1 of 35
step 2 of 35
step 3 of 35
ste
Chapter7.1
Problem 1E
Find the three-digit decimal floating-point representation
of each of the following numbers:
(a) 2312
(b) 32.56
(c) 0.01277
(d) 82,431
Step-by-step solution
step 1 of 4
step 2 of
Chapter7.3
Problem 1E
Let
(a) Reorder the rows of (A|b) in the order (2, 3, 1) and
then solve the reordered system.
(b) Factor A into a product P T LU, where P is the
permutation matrix corresponding
Chapter7.5
Problem 1E
For each of the following vectors x, find a rotation matrix
R such that Rx = |x| 2 e 1 :
Step-by-step solution
step 1 of 3
step 2 of 3
step 3 of 3
Problem 2E
Given x R 3 , define
Chapter5.1
Problem 1E
Find the angle between the vectors v and w in each of the
following:
(a) v = (2, 1, 3) T , w = (6, 3, 9) T
(b) v = (2,3) T , w = (3, 2) T
(c) v = (4, 1) T , w = (3, 2) T
(d) v =
Chapter5.3
Problem 1E
Find the least squares solution of each of the following
systems:
step 1 of 7
step 2 of 7
step 3 of 7
step 4 of 7
step 5 of 7
step 6 of 7
step 7 of 7
Problem 2E
For each of your
Chapter6.7
Problem 1E
For each of the following matrices, compute the determinants of all the leading principal
submatrices and use them to determine whether the matrix is positive definite:
Step-by-s
Chapter6.6
Problem 1E
Find the matrix associated with each of the following
quadratic forms:
Step-by-step solution
step 1 of 4
(a)
Consider the following quadratic form.
(1)
To find the matrix associ
Chapter2.1
Problem 1E
Let
(a) Find the values of det(M 21 ), det(M 22 ), and det(M 23 ).
(b) Find the values of A 21 , A 22 , and A 23 .
(c) Use your answers from part (b) to compute det(A).
Step-by-s
Chapter1.2
Problem 1E
Which of the matrices that follow are in row echelon
form? Which are in reduced row echelon form?
Step-by-step solution
step 1 of 12
A matrix is said to be in row echelon form
(i
MATH 304
Linear Algebra
Spring 2011
Instructor: Jean Marie Linhart
Practice for Exam 2
Make sure you understand what some of the basic terms are. In your own words dene the
following terms. Since you
MATH 304
Linear Algebra
Spring 2011
Instructor: Jean Marie Linhart
Practice for Exam 3
Make sure you understand what some of the basic terms are. In your own words dene the
following terms. Since you
MATH 304: Linear Algebra
Instructor:
Dr. Jean Marie Linhart
http:/www.math.tamu.edu/~jmlinhart/m304
Practice Problems before Exam 2
Instructions: You dont have to hand these in, but you will want to p
Version 084 EXAM01 gilbert (57245)
This print-out should have 15 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
10.0 points
Determine
Version 081 EXAM02 gilbert (57245)
This print-out should have 13 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
001
Consequently,
6
10
X