Linear Algebra _____ Math 413/513 _____ Section 001 ______ Spring 2016

Syllabus (updated, some misprints fixed)

Calendar (tentative)

_________ HW #1 __________ Due Jan 29.

Section 1.C.

Problems 1(all), 7, 8, 10, 19, 23

Additionaly, for MATH 513:

6(all), 20.

_________ HW #2 __________ Due Feb 12

Section 2.A

Problems 1, 6, 7 (You cannot use theory of Sections 2.B and 2.C)

Section 2.B

Problems 3(a)-(c), 6 (You cannot use theory of Section 2.C)

Section 2.C

Problems 2, 6(a)-(c), 12

Additionaly, for MATH 513:

Section 2.B problem 7, Section 2.C problem 8(all).

_________ Exam 1, Feb 17

Preparation guide

_________ HW #3 __________ Due March 4.

Section 3.A

Problems 4, 11 (You cannot use theory of Sections 3.B, 3.C, etc)

Section 3.B

Problems 1, 2, 5, 6, 12, 13 (You cannot use theory of Sections 3.C, 3.D, etc)

Section 3.C

Problem 5, 12

Section 4

Problem 5

Section 5.A

Problem 2, 7, 10

Problem:

Suppose operator T on Rn is defined by the formula T v = A*v, where v is a vector column from Rn,
A is (nxn) matrix, and A*v is a standard matrix-vector multiplication. Show that T is a linear
transformation (operator), and find the matrix of T with respect to the canonical basis of Rn.

Additionaly, for MATH 513:

Section 3.A problem 13
Section 3.B problem 25
Section 4 problem 6

_________ HW #4 __________ Due March 11

Section 5.A

Problems 12, 15, 21, 24(a), 29 (You cannot use theory of Sections 5.B, 5.C, etc)

Section 5.B

Problems 1, 2, 3 (You cannot use theory of Section 5.C)

Additionaly, for MATH 513:

Section 5.B problem 8

_________ Exam 2, March 21

Preparation guide


_________ HW #5 __________ Due March 25

Section 5.C

Problems 1, 8, 11; 12

Section 6.A

Problems 4, 5

_________ HW #6 __________ Due April 8

Section 6.A

Problem 11

Section 6.B

Problems 2, 4

Section 6.C

Problems 4, 5, 11

_________ HW #7 __________ Due April 18

Section 7.A

Problems 3, 5, 16, 17

Hint for problems 16, 17:
Use theorems 7.7 and 7.20; first, prove null T = null T*

Section 7.B

Problems 2, 3


_________ Exam 3, April 22

Preparation guide



_________ HW #8 __________ Due May 4, or 5, or 6

Section 7.B

Problem 4

Section 7.C

Problems 2, 7

Section 7.D

Problems 4, 5

Additionaly, for MATH 513:

Section 7.D, Problem 1
Hint Find an orthonormal basis of eigenvectors for T*T, then construct positive root of T*T



Final Exam is scheduled for Monday, May 9, 1:00 – 3:00 pm, at the usual room.

Preparation guide