Math 307: Problems for section 4.14.2
March 17, 2009
1. For the following matrices nd
(a) all eigenvalues
(b) linearly independent eigenvectors for each eigenvalue
(c) the algebraic and geometric mult
Math 307: Problems for section 1.2
February 2, 2009
Many problems in this homework make use of a few MATLAB/Octave .m les that are provided on
the website. In order to use them, make sure that the les
Math 307: Problems for section 4.2
1. (i) What can you say about the diagonal elements of a Hermition matrix?
(ii) Show that if A is an n n matrix such that v, Aw = Av, w then A is Hermitian.
(i) Diag
Math 307: Problems for section 1.3
1. Write down the vector approximating f (x) at interior points, the vector approximating
xf (x) at interior points, and the nite dierence matrix equation for the ni
Math 307: Problems for section 4.2
November 14, 2012
1. (i) What can you say about the diagonal elements of a Hermition matrix?
(ii) Show that if A is an n n matrix such that v, Aw = Av, w then A is H
Math 307: Problems for section 4.2
November 23, 2009
1. The matrix
6
1
A = 2
2
1
1
5
2
1
2
2
2
3
1
2
2
1
1
3
2
1
2
2
2
3
has positive eigenvalues. Use the power method to nd the largest and the smalle
Math 307: Problems for section 2.2
October 16, 2012
Problem: The following formula matrix occurs in a chemical system given by a rock sample
[3]. The elements are Si, Al, Fe, Mg, K, H and O. The speci
Math 307: Problems for section 2.1
October 4, 2009
1
1
1
0
0
2 0 1 0 4
1. Are the vectors 1, 2, 3 , 2, 9 linearly independent? You may use MAT
2 1 2 0 7
1
1
0
1
3
LAB/Octave to perform calculat
Math 307: Problems for section 2.1
October 16, 2014
0
0
1
1
1
2 0 1 0 4
1. Are the vectors 1, 2, 3 , 2, 9 linearly independent? You may use MAT
2 1 2 0 7
3
1
0
1
1
LAB/Octave to perform calcula
Math 307: Assignment 4
1. Let D be the following incidence matrix:
1 1
0
0
0 1 1
0
0 1 1
D= 0
0 1 0
1
1
0
0 1
Using MATLAB/Octave (or otherwise) compute rref (D) and nd the bases for N (D),
C (D) a
Math 307: Problems for section 2.3
October 16, 2012
1. Let D be the incidence matrix in the example done in the course notes.
1 1
0
0
0 1 1
0
0 1 1
D= 0
0 1 0
1
1
0
0 1
Using MATLAB/Octave (or othe
Math 307: Problems for section 1.2
Many problems in this homework make use of a few MATLAB/Octave .m les that are provided on
the website. In order to use them, make sure that the les are in the same
Math 307: Problems for section 1.3
1. Write down the vector approximating f (x) at interior points, the vector approximating
xf (x) at interior points, and the nite dierence matrix equation for the ni
Math 307: Problems for section 3.2
March 7, 2011
1. Review of complex numbers:
(a) Show that |zw| = |z|w| for any complex numbers z and w.
(b) Show that zw = z w for any complex numbers z and w.
(c) S
Math 307: Assignment 6
Please look at the Course News to see which of the follwing problems need to be solved. Denitely,
solving all of the problems would be helpful for the midterm exam but it is not
Math 307: Problems for section 2.1
October 4, 2009
0
1
0
1
1
2 0 1 0 4
1. Are the vectors 1, 2, 3 , 2, 9 linearly independent? You may use MAT
2 1 2 0 7
3
1
1
0
1
LAB/Octave to perform calculat
1
University of British Columbia
Math 307, Section 201
Midterm 1
Date: February 13, 2012
Time: 12:00 - 12:50pm
Name (print):
Student ID Number:
Signature:
Instructor: Richard Froese
Instructions:
1. N
1
University of British Columbia
Math 307, Section 201
Midterm 1
Date: October 5, 2012
Time: 12:00 - 12:50pm
Name (print):
Student ID Number:
Signature:
Instructor: Richard Froese
Instructions:
1. No
Chapter I
Linear Equations
1
I.1. Solving Linear Equations
Prerequisites and Learning Goals
From your work in previous courses, you should be able to
Write a system of linear equations using matrix n
Math 307: Problems for section 1.1
February 2, 2009
1. Use Gaussian elimination to nd the solution(s) to Ax = b where
11
1
1
1
1234
1 1 1 1
1
1 2 3 4
(b) A =
(a) A =
1 1 0
5 6 7 8 b = 1 ,
0
00
1
1
Math 307: Problems for section 3.33.5
March 16, 2009
1. Review of complex numbers:
(a) Show that |zw| = |z |w| for any complex numbers z and w.
(b) Show that zw = z w for any complex numbers z and w.
Math 307: Problems for section 3.13.2
March 3, 2009
1. Use the CauchySchwarz inequality for real vectors to show
2
x+y
( x + y )
2
Under what circumstances is the inequality an equality?
x + y, x + y
Math 307: Problems for section 2.1
February 2, 2009
0
0
1
1
1
2 0 1 0 4
1. Are the vectors 1, 2, 3 , 2, 9 linearly independent? You may use MAT
2 1 2 0 7
3
1
0
1
1
LAB/Octave to perform calcula
Math 307: Problems for section 2.3
March 2, 2009
1. Let D be the incidence matrix in the example done in the course notes.
1 1
0
0
0 1 1
0
0
0 1 1
D=
0 1 0
1
1
0
0 1
Using MATLAB/Octave (or otherwi
Linear Subspace Design for Real-Time Shape Deformation
Yu Wang1
1
University of Pennsylvania
Alec Jacobson2,3
2
Columbia University
Jernej Barbic4
3
ETH Zurich
Ladislav Kavan1
4
University of Southern
Quiz 2 MATH 307, APPLIED LINEAR ALGEBRA
SECTION: NAME: gwtwmww STUDENT ID#:
Problem 1. (6 points.) Consider three data points (mmyg) : (0,0),(x1,y1) =
(1, 3) (1:2, yg) 2: (3, 1). We are looking for an
Math 307 (Section 201) Midterm Examination
Instructor: Ozgur Yilmaz
February 17, 2017
Name
Student Number
1
21
2
14
3
12
4
13
Total
60
- Be sure that this examination has 10 pages. Write your name on
Math 307: Problems for section 1.3
1. Write down the vector approximating f (x) at interior points, the vector approximating
xf (x) at interior points, and the finite dierence matrix equation for the