MATH 436 LINEAR ALGEBRA
MIDTERM 1: 30 POINTS TOTAL
NAME:
START TIME:
You have 60 minutes.
END TIME:
For problem 1, you write definitions.
For problem 2, you need only circle true or false, no work needs to be
shown and work will not be graded.
For problem
MATH 436 LINEAR ALGEBRA
PRACTICE QUIZ 0
NAME:
This quiz is a chance to practice printing and uploading. Please upload
it to the Practice Quiz Drop Box. Your Lesson 1 quiz will become available
after you submit your homework.
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MATH 436 LINEAR ALGEBRA
HOMEWORK 1
Solutions
Reading: pages 1-20 of Axler, Linear Algebra Done Right, Third Edition.
Please be sure you have the Third Edition, not the second.
The work in Problems 1-5 amounts to working through the axioms to
check each on
MATH 436 LINEAR ALGEBRA
HOMEWORK 5
Solutions
Assigned June 20, due June 26 AOE.
Problem 1. Prove that the composition of injective linear maps, when it is
defined, yields an injective linear map.
Suppose f : a b and g : B C are both injective and (g f )(v
MATH 436 LINEAR ALGEBRA
HOMEWORK 3
Solutions
Assigned May 30, due June 5 AOE.
Problem 1. Prove that if (v1 , . . . , vn ) spans V , then so does the list of
differences
(v1 v2 , v2 v3 , . . . , vn1 vn , vn )
We must write v in terms of the list of differe
MATH 436 LINEAR ALGEBRA
HOMEWORK 6
Solutions
Assigned June 27, due July 3 AOE.
Problem 1. Prove the distributive properties for matrix addition and multiplication (when the multiplication makes sense).
Suppose A, B, C are matrices such that A(B + C) makes
MATH 436 LINEAR ALGEBRA
MIDTERM 2: 60 POINTS TOTAL
NAME:
START TIME:
You have one hour.
END TIME:
For problem 1, you write definitions.
For problem 2, you need only circle true or false, no work needs to be
shown and work will not be graded.
For problems
MATH 436 LINEAR ALGEBRA
HOMEWORK 7
Solutions
Assigned July 5, due July 11 AOE.
Problems 1-3 are review problems - dont need to hand these in
Problem 1. Suppose V is finite-dimensional and f : V W is a surjective
linear map. Show there exists a subspace U
MATH 436 LINEAR ALGEBRA
HOMEWORK 2
Assigned 5/23, due 5/27 AOE.
We work through proving some properties of vector spaces, and look at
sums and direct sums of subspaces of a vector space.
Problem 1. Prove that the intersection of any collection of subspace
MATH 436 LINEAR ALGEBRA
HOMEWORK 1
Reading: pages 1-20 of Axler, Linear Algebra Done Right, Third Edition.
Please be sure you have the Third Edition, not the second.
The work in Problems 1-5 amounts to working through the axioms to
check each one. This re