Math 313/513, Homework 1 (due Thurs. Jan. 19)
Name:
313 or 513 (circle)
Reading
Section 1.1 of Strang.
Book problems
Math 313: From section 1.1: 1, 2, 5, 6, 13.
Math 513: all of the above, plus problem 29
MATLAB problems
1. Do you have regular access t
Math 313 Homework 7
Due: 4/1
1
Reading
Skim Sections 6.1 and 6.2 of the book.
2
Book problems
1. Section 6.1: 3,21,27,29
2. Section 6.2: 1,2,6,9,18
3. Show that A is diagonalizable if and only if A is similar to a diagonal matrix. (Do not forget
to prove
Math 313 Homework 0
Due: Never
1. Skim Chapter 1 and Section 2.1 of the book.
2. Get started with MATLAB/OCTAVE. Learn how to do the basic operations with vectors and matrices
we discussed in class with MATLAB. As resources you can use the MATLAB primer (
Math 313 Homework 6
Due: 3/18
1
Reading
Skim Sections 5.1 to 5.3 of the book.
2
Book problems
1. Section 5.1: 2,4,5,13,14,18
2. Section 5.2: 1,4,9,16,34
3. Let An be the determinant of the tridiagonal
4
2
A4 =
0
0
Show that An = 2n (n + 1).
4. Sectio
Math 313 Homework 3
Due: 2/12
1
Reading
Skim Sections 3.2-3.6 of the book.
2
Book problems
1. Section 3.2: 1,2,3,4,9
2. Section 3.4: 4,5,16,24,34,36
3. Section 3.5: 2,3,5,8
3
Matlab
Most matrices that occur in applied mathematics and engineering are spars
Math313: Computational Linear Algebra,
Spring 2016
Course Information
Instructor: Michael Wibmer
Office: 4N61 in DRL
Office Hours: Wednesday 2-3 PM and Thursday 11-12 AM
E-mail: [email protected]
Office phone: (215) 573-1029
Midterm Exams: Wednesday F
Math 313 Homework 1
Due: 1/29
1
Reading
Skim Sections 2.2-2.4 of the book.
2
Book problems
1. Section 2.1: 26, 29, 30 (For problems 29 and 30 it suffices to write down the vectors and
name the asked for property.)
2. Section 2.2: 6,7
3. Section 2.3: 1,3,4
Math 313 Homework 4
Due: 2/26
1
Reading
Skim Sections 4.1,4.2 and 8.2 of the book.
2
Book problems
1. Section 4.1: 3,4,21,22
2. Let P be an n n matrix such that P 2 = P and P T = P . Show that P is the projection
onto a subspace of Rn .
Hint: If P is inde
MATLAB/OCTAVE Primer
Ill just say MATLAB to mean MATLAB or OCTAVE. When you first open MATLAB
you will encounter a prompt looking like:
>
After entering a command, hitting enter signals to MATLAB that you would like it to perform the operation. Try 3 + 5.
Math 313 Homework 2
Due: 2/5
1
Reading
Skim Sections 2.5-3.1 of the book.
2
Book problems
1. Section 2.5: 2,12,25,30,40
2. Let B be a square matrix such that B 4 is the zero matrix. Prove that A = I + B is invertible
with inverse A1 = I B + B 2 B 3 + B 4
Math 313 Homework 8
Due: 4/8
1
Reading
Skim Section 6.3 of the book.
2
Book problems
1. Let A be a 7 7 matrix of rank 5. Assume it is known that 3 and 4 are eigenvalues of A. Is
A diagonalizable? (Justify your answer.)
2. Section 6.3: 1,4,6,8,10,11,12,28,
Math 313 Homework 5
Due: 3/4
1
Reading
Skim Sections 4.3 and 4.4 of the book.
2
Book problems
1. Section 4.3: 1,2,9,12,28
2. Assume that Q1 , Q2 Rnn are orthogonal. Show that Q1 Q2 is orthogonal.
3. Section 4.4: 4,18,21,23
3
Matlab
Do Problem 5.12 on page
Math 313/513, Homework 2 (due Thurs. Jan. 26)
Name:
313 or 513 (circle)
Reading
Skim section 2.1 of Strang, read section 2.2.
Book problems
Math 313: From section 2.1: 26, 27, 28. From section 2.2: 10. Also the
problems below:
1. Find the reduced echelo
Math 313/513, Homework 6 (due Tues. Feb. 28)
Name:
313 or 513 (circle)
Reading
Read sections 5.15.2
Book problems
Math 313:
1. Find bases
1
A= 1
3
for the column space and
4
12
4 ,
B= 0 2
12
00
null space of the
3
3 ,
C=
3
following matrices:
2 4 2 4
2
Math 313/513, Homework 7 (due Thurs. Mar. 15)
Name:
313 or 513 (circle)
Reading
Read section 6.1 of your text, and take a look at the article The Linear Algebra
Behind Google by Bryan and Leise (linked on the course web page).
Book problems
Math 313:
Se
Math 313/513, Homework 8 (due Thurs. Mar. 22)
Name:
313 or 513 (circle)
Reading
Read sections 6.2, 6.3, and the rst four pages of 4.2
Problems
Math 313:
Section 6.2, problem 1 (show your work)
Section 6.2, problem 4 (explain your answers)
Section 6.2
Math 313/513, Homework 9 (due Thurs. Mar. 29)
Name:
313 or 513 (circle)
Reading
Read sections 4.1 4.4 of Strang.
Problems Math 313:
1. Strang, section 4.1, problem 4
2. Strang, section 4.1, problem 11 (he is referring to the four subspaces)
3. Strang, se
Math 313/513, Homework 10 (due Thurs Apr. 12th)
Name:
313 or 513 (circle)
Reading
Read sections 8.5 and 6.4 of Strang.
Problems Math 313:
1. Strang, section 8.5, problem 1
2. Strang, section 8.5, problem 2 (use the L2 inner product we discussed in class)
function [lambda, x] = largest_eig(A)
%Obtaining number of rows/columns of input matrix
[m,n]=size(A);
%Creating a random vector of length n
vec1=rand(n,1);
%Creating a normalized random vector of length n
x0=vec1/norm(vec1);
%Setting tolerance
tol=1e-6;