Math 67A Homework 4 Solutions
Joe Grimm
March 22, 2012
1
Chapter 6 CWE
6.1 Dene the map T : R2 ! R2 by T (x, y) = (x + y, x).
(a) Show that T is linear.
(b) Show that T is surjective.
(c) Find dim(null(T ).
(d) Find the matrix for T with respect to the ca
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Math 67 Quiz 2 Solution
Joe Grimm
January 28, 2012
1 Show that W = cfw_(x, y, z) : x + y + z = 0 is a subspace of R3 .
solution A subspace of a vector space is a subset of a vector space that is closed under scalar multiplication
and vector addition. To c
Math 67A Quiz 3 Solution
Joe Grimm
February 14, 2012
Problem Let V be a vector space over F and suppose that cfw_v1 , v2 , ., vn is linearly independent. Prove or
disprove: cfw_v1 v2 , v2 v3 , ., vn1 vn , vn is also linearly independent.
Solution The se
Math 67A Homework 2 Solutions
Joe Grimm
February 14, 2012
4.3 For each of the following sets, either show that the set is a subspace of C(R) or explain why it is not a
subspace.
(a) The set cfw_f 2 C(R)|f (x) 0, 8x 2 R
(b) The set cfw_f 2 C(R)|f (x) = 0
(
MAT067
University of California, Davis
Winter 2007
Linear Maps
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (February 5, 2007)
As we have discussed in the lecture on What is Linear Algebra? one of the main goals of linear algebra is the characteriza
MAT067
University of California, Davis
Winter 2007
The Fundamental Theorem of Algebra
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (February 13, 2007) The set C of complex numbers can be described as elegant, intriguing, and fun, but why are complex
MAT067
University of California, Davis
Winter 2007
Notes on Solving Systems of Linear Equations
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (March 8, 2007)
1
From Linear Systems to Linear Maps
We begin these notes by reviewing several dierent conve
MAT067
University of California, Davis
Winter 2007
Permutations and the Determinant
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (March 12, 2007)
1
Introduction
Given a positive integer n Z+ , a permutation of an (ordered) list of n distinct objects
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MAT067
University of California, Davis
Winter 2007
Eigenvalues and Eigenvectors
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (February 12, 2007)
In this section we are going to study linear maps T : V V from a vector space to itself. These linear ma