Example 5
4.1 The VectorSpoce R3 237
Let V bethe set ofall vectors (x, y) in]?!2 such that-x +3; 2 1. Thus V isthe straight
line-that passes thrOugh the unit points on the x- and yaxcs. Then 11 = (1,
3) a) (15 pts.) Let P2 be the vector space of all polynomials of degree less than or equal to
2. Find all values of a such that the polynomial x2 9x +1 6 P2 is 1_1_ot in the
subspace of P2 spanned by
MATH 225
2013 - 2014 Fall
Lab Assignment #2 Solutions
Q1) a)
dsolve('Dx = x - 1')
ans =
C2*exp(t) + 1
b)
dsolve('Dx = x - 1','x(1) = a')
ans =
(exp(t)*(a - 1)/exp(1) + 1
c)
t = -2 : 0.001 : 1;
a = 2;
MATH 225
2013 - 2014 Fall
Lab Assignment #1
Solutions
BASICS
3) The workspace consists of the set of variables built up during a session of using the MATLAB
software and stored in memory. You add vari
MATH 225
2013 - 2014 Spring
Lab Assignment #1
Due date: March 3, Monday, for all sections.
IMPORTANT
Submit your homework as a hardcopy to your instructor.
Homework must be turned in to your instructo
PHYS 101 General Physics-I, Final Exam
Duration: 125 minutes
January 15, 2009
NAME:. Section:.
Q.1 (20)
Q.2 (20)
Q.3 (20)
Q.4 (20)
Q.5 (20)
Total (100)
You must sign the Honor Code for your exam to be
Q.1
Grading: (a) 10, (b) 4, (c) 6
points
A uniform beam 9.00 m long, weighing
300 N, rests symmetrically on two
supports 5 m apart. A boy weighing
600 N starts at point A and walks
toward the right.
(
BILKENT UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2011-2012
FOURTH HOMEWORK ASSIGNMENT
December 2, 2011
Due Date:
December 12, 2011
Name
:
.
Id. No
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA: Final Exam: May 24, 2006
Final Exam Solutions
1.a) Let A be an n n matrix and k is a (constant) scalar. Show that
the set of all vectors v such tha
MATH 225: DIFFERENTIAL EQUATIONS AND LINEAR
ALGEBRA
Second Midterm Exam Solutions
1. Prove the following statements: 1.a) Let A be an n n invertible matrix. Then
the homogeneous linear system Ax = 0 h
Fla \
sou-kw to 45 Z
1 2 3 4 0 O
1) a) ( 15 pts.) Let B: O 1 2 and C = 3 g 0 be two 3x3 matrices.
O 0 1 5 0 1
Compute the following and write the necessary rules. Show your work.
i)( 3 pts.) dew; B 12
Linear Algebra & Differential Equations
2015-2016 Fall Semester
THIRD HOMEWORK ASSIGNMENT
Due Date: December 1, 2015
Name: . gochquKEY
Id. No. : .
Section: .
Department: : .
IMPORTANT
0 This homework
3.] Introduction to Linear Systems 155
Then substitution of x = O in (19) and (2C!) Yields the linear system
A+ 3:7
But33:9
that we readily solve for A = 5, B = 2. It follows that'the particular solut
BILKENT
UNIVERSITY
Mathematics Department
Math225 Differential Equations & Linear Algebra
Summer School 2016-2017
FIRST HOMEWORK ASSIGNMENT
June 15, 2017
Due Date:
June 19, 2017
Name
:
.
Id. No.
:
.
BILKENT
UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Summer School 2016-2017
SECOND HOMEWORK ASSIGNMENT
June 18, 2017
Due Date:
June 22, 2017
Name
:
.
Id. No.
:
.
S
74 Chapter 1 First-Order Differential Equations
m Problems
Find genera! solutions of the di'ereniiui equations in Pm:-
iems 1 through 30. Printer denote derivatives with reared. to x
throughout.
1- (x
Example 9
1.4 Seporoble Equations and Applications 43
In the case of an upright cylindrical tank with constant crosssectional area A, Tor-
ricellis law in Eq. (24) takes the form
d: _
E "C
with c 2 HA
56 Chapter 1 First-Order Differential Equations
Substitution of x(cfw_) = '90 gives C = (9cfw_I), so the amount of salt in the tank at
timeris
xi?) = 2(90 + 1) -
(90 + t)?"
The tank-is full after 30 m
dy x
1) Let a 6 y( y _ 2) be the given initial value problem.
y(2) = 1
a) (10 pts.) Using Existence and Uniqueness Theorem show that the initial value
problem has a unique solution.
b) (7 pts. ) Find
4‘
. . m . A. by" ,_ 2 \I
13 COHSIdST the (hi erenual equauon :4 = ~er + 2x x 4. y t X E
at
4 _. , V . . . a. .1 . 2
a) {113 pts,) Solve th1s d1fferent1a1 equatlon by geangjﬁgmegmstaggtmn u = x + y.
MATH 225 Linear Algebra and Differential Equations
Fall 2015
Homework 2
Due Date: November 10th, 2015
Name: .
ID Number: .
Department: .
Rules:
1. Include this page in your homework as the
Math 225
Differential Equations & Linear Algebra
Fall Semester 2014-2015
SECOND HOMEWORK ASSIGNMENT
October 23, 2014
Due Date: October 30, 2014
Name : .
Id. No. : .
Section : .
Department :.
IMPORTANT
ECON 225 - Exercise Set 02
November 2017
0.1
Inner Product and Norm
1. [SB, 10.5]
2. [SB, 10.6]
3. [SB, 10.19] For a rectangular 30 40 50 box, nd the angle that the largest
diagonal makes with the 40
BILKENT
UNIVERSITY
Mathematics Department
Math225 Dierential Equations & Linear Algebra
Fall Semester 2017-2018
FIRST HOMEWORK ASSIGNMENT
October 6, 2017
Due Date:
October 13, 2017
Name
:
.
Id. No.
: