MATH10260 Linear Algebra for Engineers
Problem Set 2: Polynomials and Complex Numbers.
1. Check that 2 is a root of the polynomial
P (x) = x4 + 4x3 16x 16 .
Compute the multiplicity of this root. Does
1. A pharmaceutical company produces a drug from two different compounds, A and B.
Each compound contains the same three active ingredients (AI1, AI2 and AI3) but in
different proportions.
The drug re
Question 1
A small company is involved in the daily production of two simple products but has not up
until now analysed the production output and assessed the best product mix in terms of short
term p
Question 1
The management of ABC company have decided to deploy a scientific approach to their
decision analysis given the complexities involved in their operations and the potential
for greater effic
1. A company wishes to estimate the profit from two new products. The estimated
cost of producing the first product is 3 per unit and it is expected to sell for 5
per unit while the second product cos
1.
(a) Explain what you understand by the terms feasible region and binding constraints in
respect of linear programming.
(3 Marks)
(b) A pharmaceutical company produces two types of pain relief table
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
B
C
D
E
F
G
H
I
Special Products Co. Break-Even Analysis
Data
Unit Revenue
$2,000
Fixed Cost $10,000,000
Marginal Cost
$1,000
Sales Foreca
Microsoft Excel 16.0 Feasibility Report
Worksheet: [cafeteria_mine_solver.xlsx]Sheet1
Report Created: 10/14/2016 5:23:29 PM
Constraints Which Make the Problem Infeasible
Cell
Name
Cell Value
Formula
S
Unit Rev (in Eur)
Fixed Cost
Cost Per Unit
Sales Forecast
2,000
10,000,000
1,000
30,000
Production Q
10,000
Total Rev
Total Fixed Cost
Total Var Cost
Production Q
BEP
1.5
250,000
2,000
4,500
100
300
F
1.
MATH10260 Linear Algebra for Engineers
a) Write the number (1 + 3)4 in the form a + b 3 with rational numbers a, b.
b) Show that the number (3 + 5i)6 + (3 5i)6 is real.
1+i
2
c) Compute
2014
.
d) E
MATH10260 Linear Algebra for Engineers
Problem Set 3: Basic Properties of Complex Numbers
1. Express the following complex numbers in the form a + bi where a and b
are real numbers:
a) (1 + 3i)1
b) (1
MATH10260 Linear Algebra for Engineers
Problem Set 1: Numbers and Polynomials.
1. Write numbers represented by the following nite and periodic decimal
n
expansions in the form of reduced fraction m ,
MATH10260 Linear Algebra for Engineers
Problem Set 5: Linear systems, method of elimination, vectors and matrices
1. Solve the following linear systems by the method of elimination:
2x + 3y = 13
x + 2
MATH10260 Linear Algebra for Engineers
Problem Set 4: Exponential with complex argument, Eulers formula and
trigonometry
1. Express the following complex numbers in the form a + bi where a and b
are r
MATH10260 Linear Algebra for Engineers
Problem Set 6: Matrices and linear systems, the inverse of a matrix
1. Bring the following matrices to reduced row echelon form:
1 1
2 5
3
1 2
3 9
2 5
1 9 3
a)
SEMESTER 2 EXAMINATION 2013/2014
MATH 10260
Linear Algebra for Engineers
Dr. Patrick Murphy
Dr. Masha Vlasenko
Time Allowed: 2 hours
Instructions for Candidates
All questions have equal weight. Please
MATH10260 Linear Algebra for Engineers
Problem Set 8: Properties of Determinants
1. Consider the matrices
1
D = 1
1
2 x+1
x
3
3
3
and
1
F = 2
4
1
x .
x2
1
3
9
Find all values of x for which
a)
a1
2.
MATH10260 Linear Algebra for Engineers
Problem Set 10: Linear Independence, Dimension and Bases
1. a) Construct a basis in the vector space of 2 2 matrices over a eld K.
b) Construct a basis in the ve
MATH10260 Linear Algebra for Engineers
Problem Set 7: Determinants
1. Find the number of inversions in each of the following permutations of 5 elements
a) 52134
b) 45213
c) 42135
d) 54321
and say whic
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
B
C
D
E
F
G
H
I
J
K
L
M
Keeping Time Break-Even Analysis
Unit Revenue
Fixed Cost
Marginal Cost
Sales Forecast
Production Quantity
Data
$4,500
$250,000
$2