Math 115A - Linear Algebra
Fall, 2012, MS 5147, MWF 11:00 - 11:50
ccle.ucla.edu/course/view/12F-MATH115A-3
Instructor: David Renfrew
Email: dtrenfrew@math.ucla.edu
TA: Wutichai Chongchitmate
Email: wutichai@math.ucla.edu
Oce: MS 6164
Oce Hours: M 10-11 W
Math 115A Quiz 1
Name:
1. Let u, v, w be distinct vectors in a vector space V over F. Show that if cfw_u, v, w is a
basis for V , then X = cfw_u + v + w, v + w, w is also a basis for V .
We need to show that cfw_u + v + w, v + w, w is linearly independent
Math 115A Quiz 1
Name:
1. A function, f , from R to R is called even if f (t) = f (t) and odd if f (t) = f (t).
Let F denote the vector space of all functions from R to R, E the subset of all even
functions and O the subset of all odd functions. Show
F =E
Math 115A Practice Test
Name:
1. (a) Dene what it means for the list (v1 , v2 , . . . , vn ) to be linear dependent.
(b) Dene what it means for V to be a subspace of W .
(c) Dene what it means for T to be a linear transformation.
In book.
2. Give an examp
Math 115A Practice Test
Name:
1. (a) Dene what it means for the list (v1 , v2 , . . . , vn ) to be linear dependent.
(b) Dene what it means for V to be a subspace of W .
(c) Dene what it means for T to be a linear transformation.
2. Give an example of or
Math 115A Midterm 1
Name:
ID:
Name that you would like to be called:
You may assume standard facts about Fn , Pn (F), Mnm (F). (i.e. they are vectors spaces
of known dimension) and their standard basis. State clearly what when you are using a
theorem from
Math 115AH
Midterm I
October 29, 2010
Name:
,
Please put your last name rst and print clearly
Signature:
1.
2.
3.
4.
5.
You can use the theorems from the book or proved in class, but you should
indicate which theorems you are using. You can use the fact t
Math 115AH
Midterm I
October 26, 2011
Name:
,
Please put your last name rst and print clearly
Signature:
1.
2.
3.
4.
You can use the theorems from the book or proved in class, but you should
indicate which theorems you are using. You can use the fact that