Math 420 Midterm #1
Instructions
Provide a solution for each problem. You must justify your responses using linear
algebra concepts. You should work alone. Gathering information from any other source
except the class materials would be considered plagiari
Math 420 Midterm #2 Study Guide
Book Sections and Big Ideas
The exam is not intended to be comprehensive in terms of all material covered in class to
date. However, material from Chapter 2 will be dependent on a good understanding of
material from Chapter
Math 420 Midterm #2
Provide a solution for each problem. You must justify your responses using linear
algebra concepts. You should work alone. Gathering information from any other source
except the class materials would be considered plagiarism.
(1) [25 p
Linear Algebra Fall 2015
This syllabus is subject to change at the discretion of the instructor.
Course:
Website:
Times:
Location:
Instructor:
Oce Hours:
Math 420 (3 credits)
math.wsu.edu/faculty/tasaki/Classes/Math420/Math420.html
MWF 9:10 10:00
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Math 420 - Midterm Examination I - September 30, 2015
This exam has 4 problems. For full credit, it is necessary to Show your
work and provide your reasoning.
Problem 1 [25]
Let W = {(a1,a2,a3) E R3 :
Transmission Radiography and Tomography
A Simplied Overview
This material provides a brief overview of radiographic principles prerequisite to Lab #2 of
the Radiography and Tomography Linear Algebra Modules. The goal is to develop the basic
discrete radio
Radiography for Linear Algebra Lab 2
Radiographic Scenarios and Notation
A single-view radiographic setup consists of an area of interest where the object will be
placed, and a single screen onto which the radiograph will be recorded. A multiple-view
radi
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Math 420 - Midterm Examination I - October 9, 2013
This exam has 4 problems. For full credit, it is necessary to show your
work and provide your reasoning.
Problem 1 [10]
Let M22 (C) be the vector space of 2 2 matrices over C. Let
W = cfw_A M2
Homework #6 Linear Transformations Solutions
1. Determine whether or not each given operation is a linear transformation. As
always, justify your conclusions. Let S be the vector space of all sequences with
a nite number of nonzero entries and C(R) be the
Homework #4 Solutions
Exercise 1.4.5
Determine whether the given vector is in the span of S.
Solution: In each case determine if the given vector, say x, can be written as a
linear combination of the vectors in S = cfw_v1 , v2 , . Sometimes this is done b
Homework #7 Solutions
1. Consider the two linear transformations U, T : C C given by T (z) = z + iz
and U (z) = 2z/(1 i). Use the Corollary on page 73 to determine if U = T .
Solution. T and U are equivalent transformations if they identically transform a
Radiography for Linear Algebra Lab 1
Images as vectors
A grayscale image can be associated with a set of numbers representing the brightness of each
pixel. For example, the 2 2 pixel image below can be associated with the corresponding
array of numbers, w
Radiography and Tomography in Linear Algebra
Lab #3
In this activity, you will explore some of the properties of radiographic transformations.
In Lab #2 you found six radiographic transformation operators. The object image
consisted of four voxels and was
Transmission Radiography and Tomography Questions
Read the handout entitled Transmission Radiography and Tomography: A Simplied
Overview and then answer the following questions.
1. Given Tkj = 0.42, what does this value mean?
2. What is accomplished in th
Denition: A basis for a vector space V is a linearly independent subset of V that
generates V .
Denition: A subset of a vector space V is a basis for V if is linearly independent
and span() = V.
Theorem: If a vector space V is generated by a nite set S, t
Homework #5 Solutions
Exercise 1.6.4
Do the polynomials x3 2x2 + 1, 4x2 x + 3, and 3x 2 generate P3 (R)? Justify
your answer.
Answer: No. P3 (R) has dimension n = 4 because the standard basis cfw_1, x, x2 , x3
has four elements. Every generating set must
Math 420 ~ Midterm Examination II - October 28, 2015
For full credit, you must show your work and provide your reasoning.
Problem 1 [25]
Let P2 (R) be the vector space of real polynomials of degree at most two. Con—
sider the linear operator T : P2 (R) —>
Homework #3 Solutions
Exercise 1.3.5
Prove that A + At is symmetric for any square matrix A.
Proof: Any square matrix B is symmetric if and only if B = B t . Observe: B :=
A + At = (At )t + At = (At + A)t = (A + At )t = B t . Thus, A + At is symmetric.
Ex
Homework #1 Fields
Problem #1: Determine whether or not R is a eld with the following operations
dened for addition and multiplication, respectively.
a b = a + b and a
b = 2ab.
Problem #2: Carefully show that R is not a eld with the following operations
d
Homework #1 Solution Notes
In class, we found the matrix representation of the heat diusion operator to be
1 2
0
0
1 2
0 .
E=
.
0
1 2
.
.
.
.
.
We see that if we are want to nd the kth heat state, u(kt) in the heat diusion, we need to use
u(kt) = E k u(