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 have a blue book, write your answers
on loose sheets of p
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 aid on this exam
Printed name:MI'
Signature:
I USE) at
In-class Exam I, MATH304/506, 09/18/2012
Solutions
Question 1 (5 points)
Consider the linear system
x1 + x2 + x3 = 2
2x1 + 3x2 + 2x3 = 1
3x1 + 8x2 + 2x3 = 3
(a) Write this system as a matrixvector equation of the form Ax = b.
Solution: The linear system i
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 and p (2) = p(1).
Problem 2 (20 pts.) Let v1 = (1, 1, 1),
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Chapter2.2
Problem 1E
Evaluate each of the following determinants by inspection:
Step-by-step solution
step 1 of 3
step 2 of 3
step 3 of 3
Problem 2E
Let
(a) Use the elimination method to evaluate det(A).
(b) Use the value of det(A) to evaluate
Step-by-st
Chapter1.3
Problem 1E
If
Compute
Step-by-step solution
step 1 of 8
step 2 of 8
step 3 of 8
step 4 of 8
step 5 of 8
step 6 of 8
step 7 of 8
step 8 of 8
Problem 2E
For each of the pairs of matrices that follow, determine
whether it is possible to multiply t
Chapter1.1
Problem 1E
Use back substitution to solve each of the following
systems of equations:
Step-by-step solution
Problem 2E
Write out the coefficient matrix for each of the
systems in Exercise 1.
Reference: Exercise 1:
Use back substitution to solve
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) If the first nonzero entry in each nonzero row is 1.
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-step solution
step 1 of 8
step 2 of 8
step 3 of 8
step 4
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
case of a false statement, give an example to show that
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 completed the exam, please place
it on the table at the
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.
Notation: We may at times use the notation (x1 , x2 , .
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 of 4
Problem 2E
Let A be the matrix in Exercise 1. Use
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, 2) T , u 2 = (2, 5) T
(c) u 1 = (0, 1) T , u 2 = (1,
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 by solving the
characteristic equation, and determine
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
step 4 of 35
step 5 of 35
step 6 of 35
step 7 of 35
step 8
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 4
step 3 of 4
step 4 of 4
Problem 2E
Find the absolute
Chapter1.6
Problem 1CTA
If the row echelon form of A involves free variables, then the system Ax = b will
have infinitely many solutions.
Step-by-step solution
step 1 of 2
step 2 of 2
Problem 1CTB
Find all solutions of the linear system
Step-by-step solut
Chapter1.4
Problem 1E
Explain why each of the following algebraic rules will not
work in general when the real numbers a and b are replaced
by n n matrices A and B.
Step-by-step solution
step 1 of 4
step 2 of 4
step 3 of 4
step 4 of 4
Problem 2E
Will the
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 can look these up easily in your book and in your works
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 can look these up easily in your book and in your works