Homework 1 Solutions
1. Let a =
2
3
2
3
(i) ab =
1
2
(ii) ba =
4
and b =
1
4
1
4
. Find the matrix products (i) ab (ii) ba
= [2 1 + 3 4] = 14
12 13
2 3
3 =
=
42 43
8 12
2. Find all 2 2 matrices A = (ajk ) that commute with B = (bjk ) where bj k = j +
Homework 3 Solutions
1. Suppose that the augmented matrix for a system of linear equations has been reduced by row operations
to the given reduced row echelon form. Solve the system. Assume the variables are named x1 , x2 , .,
from left to right.
1 0 0 3
Homework 4 Solutions
1. Find the
1
(i) 0
3
rank and a basis for
2
0
0
(ii) 1
6
5
the row space and for the column space of the given matrices.
8 0 4
2 1 3
0 2 0
4 0 7
(iii)
4 0 2
5 5 5
0 4 0
1 2
(i) Applying the row operation R3 3R1 yields the RREF 0 0 .
Name:
Student Number:
Dierential Equations/ Linear Algebra
MTH 2201/2202
Midterm Test 2
Date: October 20, 2016
Duration: 60 min
Grading: 5 problems 50 points in total
Instructions:
1. NO books, NO notes, NO electronic devices besides a four function calcu
Differential Equations/ Linear Algebra
Mid term Test -II
MTH 2201
Duration: 60 min
02/27/2014
Max. Credit: 50 points
Answer all the questions. No credit will be given if only the answer is written
without showing the relevant supporting work. The numbers
Midterm Test II Solutions
These are solutions for one version of the test, so half of the class will have slightly different questions for
Problems 1-3. The solution methods do not differ significantly.
1. Solve
(a)
y0 = x
dy
=x
dx
dy = x dx
(This is sepa
Mid term Test 111
MTH 2201 11 / 12/ 2015
Duration: 50 min Max. Credit: 50_peints
Answer all the questions. No credit will be given if oniy the answer is written
without showing the relevant supporting work. The numbers at the end of each
question indica
MTH 2201/2202
Differential Equations/Linear Algebra
Homework 3: Linear Systems of Equations
1. Suppose that the augmented matrix for a system of linear equations
has been reduced by row operations to the given reduced row echelon
form. Solve the system. A
Differential Equations/ Linear Algebra
Test -I
MTH 2201
Duration: 60 min
9/11/2014
Max. Credit: 50 points
Answer all the questions. No credit will be given if only the answer is written
without showing the relevant supporting work. The numbers at the end
Practice Problems
MTH 2201
1. Find the rank and a basis for the row space and for the column space of the
given matrices.
8 0 4
1 2
0 2 1 3
0 2 0
0
0 7
(i) 0
(ii) 1 4
(iii)
4 0 2
3 6
5 5
5 5
0 4 0
2.
Evaluate the determinant
of
1 2 3
1
5 9
6
3
Homework 3:
Due Friday September 25, 2015
by 4:00 P.M.
Show all work for full credit.
Grading Scheme :
There are two points possible; two points will be awarded
for four correct solutions, one point will be awarded for three correct solutions,
and no poin
Differential Equations/ Linear Algebra
Test -I
MTH 2201
Duration: 60 min
2/5/2015
Max. Credit: 50 points
Answer all the questions. No credit will be given if only the answer is written
without showing the relevant supporting work. The numbers at the end o
MTH 2201/2202
Dr. Tenali
Fall 2015 Semester
Test II
Solutions (Version 1)
1.
Consider:
(x2 + 4)dy = (2x 8xy)dx
(a) Classify this ODE. This ODE is seperable and linear.
(b) Find the general solution.
Seperating variables and integrating gives: ln(1 4y) = C
MAP 2302 - Dierential Equations
CRN 11236 (3 credits)
Spring 2012
Instructor:
Oce:
Phone:
email:
Oce Hours:
Class Homepage:
Text:
Class Location:
Meeting Times:
Dr. Daniel Kern, Department of Chemistry and Mathematics
AB7 224
590-1261
[email protected]
TR 11