Math 343 Fall 00
Homework Assignments
Homework 01: due Thur. 08/31
Read Section 1.1 and 1.2
Section 1.2, #4, 8
Section 1.3, #5, 6
Homework 02: due Tue. 09/05
Section 1.3, #8, 9, 10
Additional problems:
#1: Find other forms of the following lines in R^2:
(a) y = 3
(b) x = 3 + 2t
y = 2 - 3t
(c) 6x - 3y = 12
(d) (2,3).(x-5,y+3)=0
#2 (Extra credit) Find the standard equation of the plane
containing points (0,1,0), (2,1,0), (0, -1, 2)
Homework 03: due Thur. 09/07
Read Section 2.3 and 2.4
Section 2.1, #2, 3, 4
Section 2.3, #2, 8
Section 2.4, #8
Homework 04: due Tue. 09/12
Section 2.1: #6, 8
Homework 05: due Thur. 09/14
#1. The miers Compnay produces small engins for several manufacturers.
The Company receives orders from two assembly plants for the Topfight
engine. Plant I needs at least 50 engines, and Plant II needs at least
27 engines. The company can send at most 85 engines to two plants. It
costs $20/engine to ship to plant I and $35/engine to Plant II. How
many engines should be shipped to each plant to minimize shipping cost?
What is the minimum cost? Set up the linear programming problem and
use Maple to solve it.
#2. For boundary value problem of ODE:
y" = -3y' + 2y + 2x + 3, 0 <= x <= 1
y(0)=2, y(1)=1
Set up the linear system for this problem using h=1/4 and n=3.
Homework 06: due Tue. 09/19
Solve the following boundary value problems of ODE's:
#1: y"+4y=cos(x), 0<= x <= Pi/2, y(0)=y(Pi/4)=0
The actual solution is y(x) = cos(x) + (sqrt(2)-1)sin(x)
#2: y" = -4y'/x -2y/x^2+2ln(x)/x^2, 1<= x <= 2, y(1) = 0.5, y(2) = ln(2)
The actual solution is y(x) = 4/x -2/x^2 + ln(x) -1.5
Download: Sample Maple solution
Homework 07: due Thur. 09/21
Section 6.1: #2, 4, 6
additional problem: Find eigenvalues and eigenvectors of the matrix
[ 0 -3 ]
[ 4 2 ]
Homework 08: due Tue. 09/26
Theoretical Exercises: #3, 7, 9, 11, 14 (choose four of them)
Homework 09: due Tue. 09/28
Section 6.2, #2, 4 and use Maple to generate 20 vectors for each
dynamical system
Homework 10: due Tue. 10/03
1. Section 6.2: Finish #2 by finding the steady state vector
2. Section 6.3: #6
3. Construct three 2x2 matrices that generate an attractor, a repellor
and a saddle point. None of the matrices contain zero entries.
Homework 11: due Thur. 10/05
1. Find the diagonalization of the following matrix by hand
[ -2 4 ]
[ 0 5 ]
2. For the matrix in problem #6, page 308, find the diagonalization
with Maple
Homework 12: due Tue. 10/10
Solve the following difference equations:
(1) ak = 3ak-1 - 2ak-2 , a0 = 2, a1 = -2, k = 2, 3, ...
(2) bk = bk-1 + bk-2/4 - bk-3/4, b0 = 0, b1 = 1, b2 = 1, k=3,4,...
Homework 13: due Thur. 10/12
Find particular solutions to the following initial value problems
#1: x1'(t) = -3x1(t) + 6x2(t)
x2'(t) = x1(t) - 2x2(t)
x1(0) = 500, x2(0) = 200
#2: x'(t) = -x(t) + 2y(t) + 2z(t)
y'(t) = 2x(t) - y(t) + 2z(t)
z'(t) = 2x(t) + 2y(t) - z(t)
x(0) = 0, y(0) = 1, z(0) = 0
Homework 14: due Tue. 10/17
Find the standard form and plot the graph using transformations
with Maple:
#1: 4x2+5y2-30y+25 = 0
#2: 2y2-8y+2x = 0
Homework 15: due Thur. 10/19
Identify and graph
1. 9x1 + x22 + 6x1x2 -10*sqrt(10)*x1 + 10*sqrt(10)*x2 + 90 = 0
2. 6x12 + 9x22 -4x1x2 -4*sqrt(5)*x1 -18*sqrt(5)*x2 = 5
Simplify by using eigendecomposition
3. x^2+y^2-2z^2+4xy+4xz+4yz = 5
Homework 16: due Tue. 10/24
Identify the quadratic surface and use Maple
to draw the graph through transformations
x12 + x22 + 2x32 - 2x1x2 + 4x1x3 + 4x2x3 = 16
Homework 17: due Thur. 09/28
Section 7.1, #2, 4, 6, 8, 14
Homework 18: due Thur. 11/02
Section 7.1: #9, 10, Find the orthogonal compliment of W=span((1,2,-1)).
Homework 19: due Tue. 11/7
Section 7.2: #2,4,6,7,8
Use Gram-Schmidt process to find orthogonal basis out of
(1,1,-1,0), (0,2,0,1), (-1,0,0,1)
Homework 20: due Thur. 11/09
Section 7.3: #2, 4, 5, 7, 8, 9
Homework 21: due Tue. 11/14
Least Squars Problems (handed out on 11/09)
#1, 2, 5
Homework 22: due Thur. 11/16
#1 Let W be the column space of
[ 1 0 ]
A = [ 2 -1 ]
[ 1 1 ]
Find the orthogonal complement of W
#2 Let v = (2,0,3). Find the projection of v into W if
W = span{ (1,-1,1), (2, 1, 0)}
Homework 23: due Tue. 11/21
Section 8.2, #4, 6, 8
Homework 24: due Tue. 11/28
#1: Find LU decomposition of
[ -2 5 0 -3 6 ]
[ 4 -7 -4 10 -12 ]
A = [ 2 4 -10 15 -9 ]
[ -2 11 -12 6 7 ]
[ -6 18 0 -8 31 ]
Show all steps of work. Do not attach Maple print out.
#2: Page 415, Problem 12
#3: Page 416, Problem 16 (a), (b).
Homework 25: due Thur. 11/30
Section 8.2, Page 415
For #15 and #16, (i) Find the QR decomposition
(ii) using the QR decomposition to solve
Ax = vector([1,1,1])
Homework 26: due Tue. 12/05
#1. Construct a 4x2 matrix and use SVD program to find the SVD
#2. Let A be a square matrix whose SVD is given, describe the
procedure of solving Ax=b using the SVD.