Math 235
Sample Midterm 1
1. Short Answer Problems
a) Let A be an m n matrix. What is (Null(A) ?
b) State the definition of an isomorphism L between two vector spaces V and W.
c) Let B = cfw_~v1 , . . . , ~vn be an orthonormal basis for an inner product
Math 235
Midterm Information
Tuesday, Nov 1st, 4:30 - 6:20 p.m
Material Covered: Chapters 7, 8, 9
- The questions on the midterm are largely based on those from quizzes, the practice
problems, and examples/problems from the course notes and lectures.
- Th
LINEAR ALGEBRA COURSE NOTES EDITION 3.0
by Dan Wolczuk
LIST OF KNOWN ERRORS.
Page 47 The second line from the bottom should be: In particular, if
a system of 2 linear equations in 2 unknowns has 2 solutions,
then it must in fact have infinitely many solut
Math 235
Sample Midterm 2
1. Short Answer Problems
a) State the Fundamental Theorem of Linear Algebra.
b) State the Rank-Nullity Theorem.
c) Let L : V U and M : U V be linear mappings such that (M L)(~x) = ~x for all
~x V. Prove that M is onto.
d) Let h ,