(a) Find an LU-factorization of A i.e. use row operations to find U, an upper triangular matrix equivalent to A and L, a lower triangular matrix such that A LU . (b) Find the determinant of A. 3 1 3 1 4 2 0 and b 1 . 2. Let A 2 2 1 4

(a) Find the determinant of A. (b) Solve the linear system Ax b by the Cramer’s rule. a 3. Let V be the set of all 2 1 real matrices v , where a and b are integers such b 3 8 1 1 that a b is even. Examples of matrices in V are , , , and . 5 2 7 1 Let the operation be standard addition of matrices and the operation be standard scalar multiplication of matrices on V. Is V a vector space? Justify your answer.

4. The following set together with the given operations is not a vector space. List the properties in the definition of a vector space that fail to hold. a V is the set of all 2 1 real matrices v , with operation be standard matrix b addition and the operation be scalar multiplication

c

a c ( a b) b c(a b) , for any real number c.

Note: This assignment must be submitted to your respective tutor (or deposit your assignment in the prescribed MAT111 pigeon-hole on the ground floor of Building G31) on or before Monday, 1 April 2013. Late submission will not be entertained.

...LINEARALGEBRA
Paul Dawkins
LinearAlgebra
Table of Contents
Preface............................................................................................................................................. ii Outline............................................................................................................................................ iii Systems of Equations and...

...Solving systems of linear equations
7.1 Introduction
Let a system of linear equations of the following form:
a11 x1
a21 x1
a12 x2
a22 x2
ai1x1 ai 2 x2
am1 x1 am2 x2
a1n xn
a2 n x n
ain xn
amn xn
b1
b2
bi
bm
(7.1)
be considered, where x1 , x2 , ... , xn are the unknowns, elements aik (i = 1, 2, ..., m;
k = 1, 2, ..., n) are the coefficients, bi (i...

...Initialise
Clear the workspace and load LinearAlgebra package
> restart;
> with(LinearAlgebra):
If you want practice at hand calculation you should use the worksheet "Interactive Gaussian Elimination" (see Menu)
Enter the matrix of coefficients and right-hand side vector
You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View, Palettes)
> A:=<<4 | 2 | 3 | 2> , <8 | 3 | -4 | 7> , <4 | -6 | 2 |...

...Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information...

...arithmetic and algebra. His works was a significant source for mathematical insight for centuries to come in both the east and west.
Al-Khwarizmi and his colleagues, the Banu Musa, were scholars at The House of Wisdom in Baghdad. Their task there included the translation of Greek scientific manuscripts. In addition, they worked on algebra, geometry, and astronomy. Under the patronage of Al-Mamum, he dedicated two of his texts to the Caliph- his treatise on...

...sense that there are many aspects of Algebra that the majority of people do not use on a daily basis. I think that this fact is what leads people to the false conclusion that Algebra is useless.
To better understand our topic, let’s define what we mean when we say “Algebra”. Webster’s dictionary defines Algebra as “a form of mathematics dealing with symbols and equations.” A guest in the mathematics forum on xpmath.com states that...

...GUIDE
With sample test questions
MATHEMATICS / ALGEBRA |
Key Words and Converting Words to EquationsFractions Adding, subtracting, multiplying, dividing Simplifying Writing decimals as fractions StatisticsReading Tables and ChartsExponentsPre-Algebra and Algebra Special notation for multiplication and division with variable Algebra word problems Order...

...make mathematics, especially the algebra as enjoyable as possible to those freshmen students in high school level and allow them to be productive as a student upon integrating the computer-assisted program in their studies.
Algebra is a branch of mathematics concerning the study of structure, relation, and quantity. Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. This only means...

## Share this Document

Let your classmates know about this document and more at StudyMode.com