Solving Cubic Equations
First, write your equation as a polynomial:
A V3 + B V2 + C V + D = 0
Method 1: Iteration
1.) Write the equation as V=f(V)
V = -(1/C) (A V3 + B V2 + D)
2.) Pick an initial guess for V0 (eg 0, Vig, etc.) and evaluate:
V1 = -(1/C) (A
MATH10212 Linear Algebra B Homework 10
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay, Linear Algebra and its Applications. Pearson, 2006 (or other editions).
Normally, homework assignments will consist of some odd numbered exe
MATH10212 Linear Algebra B Homework 1
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay Linear Algebra and its Applications. Pearson, 2006. ISBN 0-521-28713-4.
Normally, homework assignments will consist of some odd numbered exerc
MATH10212 Linear Algebra B Homework Week 3
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay Linear Algebra and its Applications. Pearson, 2006. ISBN 0-521-28713-4.
Normally, homework assignments will consist of some odd numbered
MATH10212 Linear Algebra B Homework Week 2
Deadline: make sure that your solutions to problems 9*11* reach your supervision
class teacher 24 hours before your supervision class in Week 2.
Students are strongly advised to acquire a copy of the Textbook:
D.
MATH10212 Linear Algebra B Homework Week 4
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay Linear Algebra and its Applications. Pearson, 2006. ISBN 0-521-28713-4.
Normally, homework assignments will consist of some odd numbered
Lecture 14
Eigenvalues and Eigenvectors
Suppose that A is a square (n n) matrix. We say that a nonzero vector v is an eigenvector (ev)
and a number is its eigenvalue (ew) if
Av = v.
(14.1)
Geometrically this means that Av is in the same direction as v, si
Chapter 7
Eigenvalues and Eigenvectors
7.1
Eigenvalues and Eigenvectors
Homework: [Textbook, 7.1 Ex. 5, 11, 15, 19, 25, 27, 61, 63, 65].
Optional Homework:[Textbook, 7.1 Ex. 53, 59].
In this section, we introduce eigenvalues and eigenvectors. This is
one
10212 Linear Algebra B Week 8 Lecture 23
10212 Linear Algebra B
Week 8 Lecture 23
University of Manchester
22 March 2017
10212 Linear Algebra B Week 8 Lecture 23
Students are strongly advised to acquire a
copy of the Textbook:
D. C. Lay. Linear Algebra an
10212 Linear Algebra B Week 8 Lecture 22
10212 Linear Algebra B
Week 8 Lecture 22
University of Manchester
20 March 2017
10212 Linear Algebra B Week 8 Lecture 22
Students are strongly advised to acquire a
copy of the Textbook:
D. C. Lay. Linear Algebra an
10212 Linear Algebra B Week 8 Lecture 24
10212 Linear Algebra B
Week 8 Lecture 24
University of Manchester
24 April 2017
10212 Linear Algebra B Week 8 Lecture 24
Students are strongly advised to acquire a
copy of the Textbook:
D. C. Lay. Linear Algebra an
10212 Linear Algebra B Week 9 Lecture 25
10212 Linear Algebra B
Week 9 Lecture 25
University of Manchester
27 March 2017
10212 Linear Algebra B Week 9 Lecture 25
Students are strongly advised to acquire a
copy of the Textbook:
D. C. Lay. Linear Algebra an
MATH10212 Coursework Test
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NAME (Please Write Clearly in BLOCK CAPITALS):
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MATH10212
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THE UNIVERSITY OF MANCHESTER
MATH10212 Linear Algebra
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09:4512:15
Answer ALL Questions in Section A
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The use of electronic calculators is NOT permitted
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P
MATH10212
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THE UNIVERSITY OF MANCHESTER
MATH10212 Linear Algebra
Thursday 17 May 2007
09:4512:15
Answer ALL Questions in Section A
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You can get for this paper 80 points maximum, which will be re-scaled to
MATH10212
Two and a half hours
THE UNIVERSITY OF MANCHESTER
MATH10212 Linear Algebra
30 May 2008
09:4512:15
Answer ALL Questions in Section A
and Two Questions in Section B
The use of electronic calculators is NOT permitted
Formula Tables NOT To Be Used
P
2014/2015
HELIN NO#:0
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Serial No#: 3504604
Names
MILLICENT CHELANGAT KILEL
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University Name
JARAMOGI OGINGA ODINGA UNIVERSITY OF SCIENCE AND
TECHNOLOGY
Email
[email protected]
MATH10212 Linear Algebra B Homework 6
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay, Linear Algebra and its Applications. Pearson, 2006 (or other editions).
Normally, homework assignments will consist of some odd numbered exer
MATH10212 Linear Algebra B Homework 10
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay, Linear Algebra and its Applications. Pearson, 2006 (or other editions).
Normally, homework assignments will consist of some odd numbered exe
HOW TO SOLVE CUBIC EQUATIONS BY FUNCTIONS
ON THE CALCULATOR
David Tacon
Although there is a formula. for solving cubic equations (see Parabola, 2nd issue
1989) it is rarely used in practice since it can be tricky to apply in even very simple cases.
(Besid
MATH10212 Linear Algebra
Lecture Notes
Last change: 30 Jan 2017
Textbook
Students are strongly advised to acquire a copy of the Textbook:
book is easily available on Amazon (this
includes some very cheap used copies)
and in Blackwells bookshop on campus.
10212 Linear Algebra B Lectures 1921
10212 Linear Algebra B
Lectures 1921
University of Manchester
13 March 2016
10212 Linear Algebra B Lectures 1921
Lecture 19: Diagonalisation
Similar matrices
A
A is similar to B if there exist an invertible matrix P su
10212 Linear Algebra B Lectures 1315
10212 Linear Algebra B
Lectures 1315
University of Manchester
27 February 2017
10212 Linear Algebra B Lectures 1315
Lecture 13: Partitioned matrices [Lay 2.4]
Example: Partitioned matrix
A
1 2 a
A = 3 4 b
p q z
A11 A12
10212 Linear Algebra B Lectures 1618
10212 Linear Algebra B
Lectures 1618
University of Manchester
06 March 2017
10212 Linear Algebra B Lectures 1618
Lecture 16: Introduction to determinants [Lay 3.1]
Introduction to determinants [Lay 3.1]
A The determina
10212 Linear Algebra B
10212 Linear Algebra B
University of Manchester
22 February 2016
10212 Linear Algebra B
Textbook
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay. Linear Algebra and its Applications. Pearson, 2006.
ISBN 0-
MATH10212 CHECKLIST
Linear Equations in Linear Algebra:
o
Systems of Linear Equations
o
Row Reduction and Echelon Forms
o
Vector Equations
o
The Matrix Equation Ax=b
o
Solution Sets of Linear Systems
o
Applications of Linear Systems
o
Linear Independen
MATH10212 CHECKLIST
Linear Equations in Linear Algebra:
o
Systems of Linear Equations
o
Row Reduction and Echelon Forms
o
Vector Equations
o
The Matrix Equation Ax=b
o
Solution Sets of Linear Systems
o
Applications of Linear Systems
o
Linear Independence
MATH10212 Linear Algebra B Homework 1
Students are strongly advised to acquire a copy of the Textbook:
D. C. Lay Linear Algebra and its Applications. Pearson, 2006. ISBN 0-521-28713-4.
Normally, homework assignments will consist of some odd numbered exerc
MATH10212 Linear Algebra B Homework Week 2
Deadline: make sure that your solutions to problems 9*11* reach your supervision
class teacher 24 hours before your supervision class in Week 2.
Students are strongly advised to acquire a copy of the Textbook:
D.