SAMPLE PROBLEMS FOR 353-Midterm 2
TRUE FALSE
PROBLEMS 1 FROM CHAPTERS 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.3.
1. For any nn matrix A, and scalar k F , we have det(kA) = k det(A).
2. det(AAT A1 ) = detA.
3.
MA 3530000160150
MA 3530000260151
GOINS
HOMEWORK ASSIGNMENT #6
Due Friday, September 30, 2016 at the start of lecture. This should be turned in at the
start of class, and should be legible and stapled
MA 3530000160150
MA 3530000260151
LESSON 6: FRIDAY, SEPTEMBER 2, 2016
GOINS
1.6: Bases and Dimension
Recap.
Theorem 1.8. Let V, +, be a vector space over a field F . Given a finite
subset = cfw_u1 , u
MA 3530000160150
MA 3530000260151
LESSON 3: FRIDAY, AUGUST 26, 2016
GOINS
1.4: Linear Combinations and Systems of Linear Equations
Recap. We showed the following result in the previous lecture.
Theore
MA 3530000160150
MA 3530000260151
LESSON 2: WEDNESDAY, AUGUST 24, 2016
GOINS
1.3: Subspaces
Definitions. Let F denote a field ; the only examples which will interest us are
Q, the collection of ration
MA 3530000160150
MA 3530000260151
GOINS
HOMEWORK ASSIGNMENT #2
Due Friday, September 2, 2016 at the start of lecture. This should be turned in at the
start of class, and should be legible and stapled.
MA 3530000160150
MA 3530000260151
LESSON 4: MONDAY, AUGUST 29, 2016
GOINS
1.5: Linear Dependence and Linear Independence
Recap. Let V, +, be a vector space over a field F , and choose a finite subset
MA353 SPRING 2012 Homework 5
This rst problem will be a lot of work. We did something similar in lecture on March 7 and
9, so you probably want your notes from those lectures handy. Its a great proble
MA353 SPRING 2012 Homework 7:Sylvesters Criterion and
Recurrence Relations
Denition 1. Let A be a matrix/linear operator. We write A > 0 if A is positive and
invertible, that is Ax, x > 0 for all nonz
MA 3530000160150
MA 3530000260151
GOINS
HOMEWORK ASSIGNMENT #1
Due Friday, August 26, 2016 at the start of lecture. This should be turned in at the
start of class, and should be legible and stapled. L
MA 3530000160150
MA 3530000260151
LESSON 5: WEDNESDAY, AUGUST 31, 2016
GOINS
1.6: Bases and Dimension
Recap. Let V, +, be a vector space over a field F , and choose a subset S = cfw_u1 , u2 , . . . ,
MA 3530000160150
MA 3530000260151
LESSON 1: MONDAY, AUGUST 22, 2016
GOINS
1.1: Introduction
2-Dimensional Vectors. Any entity involving both magnitude and direction is called a vector.
For instance, s
Solutions to Linear Algebra, Fourth Edition, Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
Jephian Lin, Shia Su, Zazastone Lai July 27, 2011
Copyright 2011 Chin-Hung Lin. Permission is gra
SAMPLE PROBLEMS FOR 353 nal
TRUE FALSE
.
1. Let W1 , W2 , and W3 be subspaces of a vector space V , then (W1 +
W2 ) W3 is a subspace of V .
2. If dim(V ) = n then any set of n-vectors is linearly inde
Math 54 Discussion Section SOLUTIONS
Rob Bayer
April 14, 2008
Dont freak out. Some of these problems are meant to be hard.
1. Prove that if A is invertible, then AB is similar to BA
AB = A(BA)A1 , so
SAMPLE PROBLEMS FOR 353-Midterm 1
TRUE FALSE
1. Let W1 , W2 , ., Wr be subspaces of a vector space V , then W1 . . .Wr
is a subspace of V .
2. Consider S1 S2 V two sets of vectors of a vector space V
MATH353-001\002
Final Exam Solution
December 9th, 2013
Instructor: CHING-JUI LAI
1
2
1. True and false. You dont need to explain the reason. Note
that a vector space V can be innite dimensional if not
Fall 2012
Exam #3 Key
Math 306
1. Denitions and Short Answer: (3 Points Each) Give a denition or short answer for each
of the following.
(a) A Subspace of a vector space V . A subset H of a vector spa
MATH353-001\002
Final Exam
December 9th, 2013
Instructor: CHING-JUI LAI
NAME:
PUID:
There are in total 200 points in this exam.
You can use both sides of the paper.
No calculator.
Mark clearly you
SUMMARY OF MA 35100: ELEMENTARY LINEAR ALGEBRA
Course Description
The following can be found here: https:/www.math.purdue.edu/academic/courses/MA35100/
Credit Hours: 3.00. Systems of linear equations,
MA353 SPRING 2012 Homework 6/Notes
1. Theorems from lecture
Recall the following items from lecture: Let T : V V be a linear operator (as always, a
nite-dimensional inner product space, either real or
Purdue University MA 353: Linear Algebra II with Applications Homework 11, due Apr. 9, Some solutions Sec. 5.4:#16: Let T be a linear operator on a finite-dimensional vector space V . (a) Prove that i
Purdue University MA 353: Linear Algebra II with Applications Homework 10, due Apr. 2, Some Solutions (I) Sec. 1.6#34: (a) Prove that if W1 is any subspace of a finite-dimensional vector space V , the
Purdue University MA 353: Linear Algebra II with Applications Homework 9, due Mar. 26, Some Solutions (I) Sec. 5.1:#17 Let T be the linear operator on Mnn (R) defined by T (A) = At . (a) Show that 1 i
Purdue University MA 353: Linear Algebra II with Applications Homework 8, due Mar. 12, Some Solutions (I) Sec. 5.1#8 (a) Prove that a linear operator T on a finite-dimensional vector space is invertib
Purdue University MA 353: Linear Algebra II with Applications Homework 7, due Mar. 5, Some Solutions sec. 2.4 #4: Let A and B be n n invertible matrices. Prove that AB is invertible and (AB)-1 = B -1
Purdue University MA 353: Linear Algebra II with Applications Homework 6, due Feb. 26, Some Solutions Sec. 2.2 #13: Let V and W be vector spaces, and let T and U be nonzero linear transformations from
Purdue University MA 353: Linear Algebra II with Applications Homework 5, due Feb. 19, Solutions Sec. 2.1 #9 Prove that there exists a linear transformation T : R2 R3 such that T (1, 1) = (1, 0, 2) an