Prof. A. Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
Geometric interpretation of some linear transformations
1. Rotation-dilations
To interpret the linear transformation
T (x) =
a b
x
b
a
a
a
r cos
in
Resume Checklist
Accomplishment-Oriented
First Impression
Is the resume inviting to read, with clear sections and
ample white space?
Does the design look professional and not like a simple
typing job?
How to calculate seasonal
index
Pick time period (number of years)
Pick season period (month, quarter)
Calculate average price for season
Calculate average price over time
Divide season average by ove
IE 7200
Supply Chain Engineering
Date:02/05/2017
Homework # 2
Problem 1.
Year
Month
Demand
(Units)
1
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
100
125
140
160
185
210
225
235
215
200
Chap 2. The Geometry of LP
In the text, polyhedron is defined as P = cfw_ x Rn : Ax b . So some
of our earlier results should be taken with modifications.
Thm 2.1:
(a) The intersections of convex se
MS-E2140 Linear Programming
Exercise 7
Thu 06.10.2016
Maari-B
Week 4
This weeks homework https:/mycourses.aalto.fi/mod/folder/view.php?id=130935 is due no
later than Sunday 16.10.2016 23:55.
Exercise
MS-E2140 Linear Programming
Exercise 4
Fri 23.09.2016
Maari-B
Week 2
This weeks homework https:/mycourses.aalto.fi/mod/folder/view.php?id=130923 is due no
later than Sunday 02.10.2016 23:55.
Exercise
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Prof. A. Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
SAMPLE EXAM 4
1. Let A =
13
. What is the area of the parallelogram spanned by the column vectors of 5I2 A?
26
2. Compute the area of the triangle wi
Prof. Alexandru Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
SOLUTIONS to EXAM 2
1. 12 points
12345
A = 1 0 1 2 3
23058
1 0 0 2 7
2
rref A = 0 1 0 3
5
0 0 1 0 1
2
(a) Find a basis for the image of A.
Col
Prof. Alexandru Suciu
MTH 1230
LINEAR ALGEBRA
EXAM 2
1. 12 points
12
1 0
Let A =
23
(a) Find a basis for
3
1
0
the
45
2 3.
58
image of A.
(b) Find a basis for the kernel of A.
(c) Find the rank and th
Prof. Alexandru Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
EXAM 1
1. 10 points
(a) Use Gauss-Jordan elimination (rref) to solve the following system of equations. Carry out
the elimination all the way,
Prof. Alexandru Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
EXAM 4
1. 12 pts
(a) Compute the area of the region enclosed by the folowing quadrilateral:
1
4
4
2
3
2
2
1
2
0
2
1
(b) Compute the area of
Prof. Alexandru Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
SOLUTIONS to EXAM 1
1. 10 points
(a) Use Gauss-Jordan elimination (rref) to solve the following system of equations. Carry out
the elimination
Prof. A. Suciu
MTH 1230
LINEAR ALGEBRA
Spring 2001
SAMPLE EXAM 2
2
1
10
4
2
2 0
1. Let A =
6 3 0 1.
2
1 2 0
(a) Find a basis for im A.
(b) Find a basis for ker A.
(c) Find rank A.
1 34
2. Let A = 4 5
1
2
3
4
5
6
7
8
Name:
NORTHEASTERN UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH 1230
FINAL EXAM
Spring 2001
Instructions: Put your name in the blanks above. Put your nal answers to each question in the
de
1
2
3
4
5
6
7
8
Name:
NORTHEASTERN UNIVERSITY
DEPARTMENT OF MATHEMATICS
MTH 1230
FINAL EXAM
Spring 2001
Instructions: Put your name in the blanks above. Put your nal answers to each question in the
de
iii) Material planning for subassembly A (level 1):
Since A is dependent on product 1, therefore the projected requirement for A in week 4 is 105
Lot size = PPB
Lead time = 1
Projected Requirement
Wee