Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2013
1
Solutions to Section 1.1
TrueFalse Review:
1. FALSE. A derivative must involve some derivative of the function y = f (x), not necessarily the rst
derivative.
2. TRUE. The initial conditions accompa
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Homage ark gcholcms
Seciiam 1.1:
1 . We have
Av=[:i][3][t]=2v.
as required.
1 3 l 4 1
2.Av=[2 2H1]=[d]=4[ 1 ]=Av
1 2 6 2 (i 2
3 AV 2 2 2 5 l = 3 = 3 l = Av.
2 l 8 l 3 l
l 1 (.1 +162
4. Since v
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
vu'vv IV! '5.
Instructions: Show your work and indicate your reasoning. You will not receive credit if
you do not clearly Show how you are obtaining your answers. Box your nal answer. Do all
work on t
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Some More Problems On Ch 8 and 9
SOLUTIONS
Problem 1. Let L := D2 x1 D + 4x2 . Verify that y(x) = sin(x2 ) is in the kernel of L.
SOLUTION: Since the operators D and D2 appear, we need to co
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Midterm III Information
Fall 2016
SOLUTIONS TO PRACTICE PROBLEMS
Problem 1. Determine whether the following matrix is diagonalizable or
not. If it is, find an invertible matrix S and a diago
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
April, 2017 Quiz 6 Name:
Math 250B
1. (10 points) Consider the dierential equation
D(D2 4D + 5)y = 653(2 392) 00393 + 2mm.
Determine an appropriate solutibn for the differential equation (1) by anni
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Problem 2.(5 points) If A is an eigenvalue of the matrix A, Show that A 5 is an eigenvalue of
the matrix A BI.
X is eValu. ul A ._> OHM2M.) :0
Of EVE/Av
Mm 5V bath 31345 _
PVT! 517: A 1' SV
[15 53
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Chapter 8:
Linear Differential Equation of order .
Section 8.1
General Theory for Linear Differential Equation.
Notations:
= interval on the real line (, ) or (, )
0 () = cfw_continuous function in
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Midterm III Information
Spring 2017
WHEN: Wednesday& Thursday, May 3&4, in class (no notes, books, calculators
I will supply a list of common annihilators.)
REVIEW SESSIONS:
Mon, May 1, 2:3
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
December 2016
Midterm III Review Session
Math 250B
SOLUTIONS
Name:
Problem 1. Suppose A is a square matrix such that
A3 2A2 + 4A + 5I = 0.
If is an eigenvalue of A, show that
3 22 + 4 + 5 = 0.
SOLUTIO
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
May 9, 2016
Midterm III
Math 250B
SOLUTIONS
Name:
Problem 1. (9 points) Decide whether the matrix A below is diagonalizable or not,
circle your answer, and show work to justify it. If the matrix is di
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Problem 1. (9 points) Decide whether the matrix A below is diagonalizable or not, circle your
answer, and show work to justify it. If the matrix is diagonalizable, nd an invertible matrix S and
a diag
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
December 2016
Midterm III Review Session
Math 250B
Name:
Problem 1. Suppose A is a square matrix such that
A3 2A2 + 4A + 5I = 0.
If is an eigenvalue of A, show that
3 22 + 4 + 5 = 0.
Problem 2. Suppos
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Group Work #4
SOLUTIONS
Spring 2017
Problem 1. Find the solution set for the given system:
2x1 x2 x3 = 0,
5x1 x2 + 2x3 = 1,
x1 + x2 + 4x3 = 0.
SOLUTION: Reduce the augmented matrix of
2 1
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Group Work #3
SOLUTIONS
Spring 2017
Problem 1. Solve the differential equation
(3x 2y)
dy
= 3y.
dx
SOLUTION: We see that this differential equation is homogeneous of degree zero, so we set y
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B
Group Work #1
SOLUTIONS
Spring 2017
Problem 1. Find all values of r such that y(t) = ert is a solution to the differential
equation
(a): y 00 + 3y 0 10y = 0.
SOLUTION: We have y 0 = rert and
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Homework Sol +20 nJ'
l 2 U
2 t 0 0 _
1. (a). T(10,5) = l 8 5 1 = 0 . Thus, x (lees belong to lxerljI).
. . J
8 16 0
l 2 l
2 4 I 2 .
(b). T(1,l) = ti 8 l = II . Thus, 3: does not belong to ixer(T).
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
H'o manner1% gallql'i'ons
m
Static n Li". 8
3. (a). n =
(b)
5; a basis for rowspacepl) is given by 1,2, 3, l 5)
m = l; a basis for colspacel) is given by [1.
I 2 3
6. (a). n. = 3; a rowechelon f
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
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Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
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Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Math 250B Introduction to Linear Algebra
and Differential Equations
MWThF 2:00pm  2:50pm: MH 416
Section 7  Class Number: 18574
_
Instructor: Michael Moretti
Email: [email protected]
Office: MH
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Name_
Class (Day/Time)_
Math 338 Exam 2
1. For each of the scatterplots shown, describe the form (linear, exponential),
direction (positive, negative), and strength (strong, moderate, weak) of the
pat
Intro to Differential Equations and Linear Algebra
MATH 250B

Spring 2010
Name_
Class (Day/Time)_
Math 338 Exam 1
1. You plan to study the reliability of hard drives from various manufacturers: one
model from each manufacturer. Amongst the manufacturers you will be studying