Math 630-102
Homework 2
Section 1.4
Problem 13 (a, b, d). By trial and error find examples
Note: this means that you are asked to guess the matrix elements, although you
may easily find a more systematic way to solve this problem. You dont have to
do part
(12 points) De_ne each of the following sets where X and Y are sets in
the universe U:
(a) X [ Y : The union of the sets X and Y , denoted X [ Y , is given
by
X [ Y := fz 2 U j z 2 X or z 2 Y g:
(b) P(X): The power set of the set X, denoted P(X), is the s
Math 630-102
Final Exam
May 3, 2007
This is a closed-book exam: notes and calculators are not allowed. Please explain your
solutions to receive full credit. Check your answers.
2 1 1 0
3
2 2 0 2 , b= 0
1. (23) Consider the linear system Ax=b with A=
Math 630-102 Homework #12 (last one) Due date: April 26, 2007
Problem 1 (5.4.10). Decide on the stability or instability of the zero equilibrium for dv/dt=w, dw/dt=v. Is there a solution that decays to zero? Draw some arrows in the phase plane (v, w) to e
Math 630-102 Homework #11 Due date: April 19, 2007
Group work on h/w assignments is not allowed. No credit is given for results without a solution or an explanation. Late homework is not accepted.
Section 5.2 Problem I. Any symmetric matrix (AT=A) satisfi
Math 630-102 Homework #10 Due date: April 12, 2007
Group work on h/w assignments is not allowed. No credit is given for results without a solution or an explanation. Late homework is not accepted.
Section 5.1 Problem I. Calculate the eigenvalues and the e
Math 630-102 Homework #9 Due date: April 5, 2007
Group work on h/w assignments is not allowed. No credit is given for results without a solution or an explanation. Late homework is not accepted.
Sections 4.3, 4.4 0 1 Problem I. Consider the matrix A= 2 5
Math 630-102
Homework #8
Due date: March 29, 2007
Group work on h/w assignments is not allowed. No credit is given for results
without a solution or an explanation. Late homework is not accepted.
Section 3.3
Problem 6. Find the projection of b onto the co
Math 630-102
Homework #6
Due date: February 29, 2007
Group work on h/w assignments is not allowed. No credit is given for results
without a solution or an explanation. Late homework is not accepted.
Section 2.6
Problem I (not in book) Show that integratio
Math 630-102
Homework 5
Due date: February 22, 2007
Group work on h/w assignments is not allowed. No credit is given for results
without a solution or an explanation. Late homework is not accepted.
Note on calculating the left null-space: As the notation
Math 630-102
Homework 4
Due date: February 15, 2007
Group work on h/w assignments is not allowed. No credit is given for results
without a solution or an explanation. Late homework is not accepted.
Section 2.2
Problem 2. Reduce A and B to echelon form, to
Math 630-102
Homework 3
Due date: February 8, 2007
Group work on h/w assignments is not allowed. No credit is given for results
without a solution or an explanation. Late homework is not accepted.
Section 1.6
Problem 6. Use Gauss-Jordan method to invert A
MATH 110, Linear Algebra, Fall 2013
Solutions to Homework #1.
Chapter 1.
1.
a
1
(a ib)
a ib
b
= 2
=
= 2
+i 2
2
(a + ib)
(a + ib)(a ib)
a +b
a +b
a + b2
3. Recall that v = (1)v. Thus (v) = (1)(1)v) = (1)(1)v = (1)v = v.
4. Suppose av = 0 but a = 0. Then v