matrcies

2. HISTORY OF MATRIX
 "Matrix" is the Latin word for womb, and it
retains that sense in English. It can also mean
more generally any place in which something is
formed or produce.

3. FOUNDER OF TERM “MATRIX”
 (3 September 1814 – 15 March 1897)
 He was an English mathematician.
 The term "Matrix“ for such arrangements was
introduced in 1850 by James Joseph Sylvester.

4. FONDER OF MATRIX THEORY
Arthur Cayley:
(16 August 1821 – 26 January 1895)
 He was a British mathematician. He
helped found the modern British school
of pure mathematics.
 The credit for founding the theory of
matrices must be given to Arthur Cayley.

5. FONDER OF MATRIX THEORY
 He introduces, although quite sketchily,
the ideas of inverse matrix and of matrix
multiplication, or "compounding" as
Cayley called it.

6. HAMILTON THEOREM
 Arthur Cayley and William Rowan Hamilton, two
mathematicians discovered a unique feature
pertaining to matrices.
 In case you have no clue about what matrices
dynamic and ever changing world of mathematics,
a matrix (plural form matrices) is a rectangular
array of numbers.
 Symbols or even expressions arranged into rows
and Columns.

7. HAMILTON THEOREM
 . Each individual number/symbol/or
expression is known as an element or
an entry.
A matrix with two rows and three
Columns is referred to as a 2*3(row by
column) (read as two by three) matrix

8. HAMILTON THEOREM
 The image shown directly below provides two
examples of matrices, a 2*3 matric and 3*2
matrix.

9. KEY POINT:
 (Chiu Chang SuanShu) gives the first known
example of the use of matrix methods to solve
simultaneous equations.

10. DEFINITION OF MATRIX
 IT is the set of real numbers arranged in
rectangular array in the form of rows and
columns .It is denoted by A, B, C etc.

11.  ROW:
The elements on the horizontal line.
Example:
 Columns:
The elements on the vertical line.
MATRIX

12. MATRIX

13. MATRIX
 Order
 The number of rows and the number of columns
is called order of matrix
 Here is an example to express it
 Example:

14. TYPES OF MATRIX
 Row Matrix:
A matrix has one row but several columns.
 Example:
Order of matrix =1×4
Column matrix:
A matrix has one column but several
rows.

15. TYPES OF MATRIX
Example:
𝟗
𝟕
𝟕

16. TYPES OF MATRIX
 Square Matric:
A matrix in which number of rows is equal to
number of columns.
 Example:
 Order of matrices A=3×3
 That boxes also show square matrix.
 Because order of boxes =3×3.

17. TYPES OF MATRIX
 Rectangular matrix:
A matrix in which number of rows is not equal to
number of columns.
 Example:
 Order of matrix =4×5

18. TYPES OF MATRIX
 This picture also shows rectangular matrix

19. TYPES OF MATRIX
 Diagonal Matrix:
A square matrix in which all elements are zero
expect diagonal elements is called “Diagonal Matrix”
 Example:

20. TYPES OF MATRIX
 Scalar matrix:
A square matrix in which all elements and zero
expect diagonal elements are same(expect one).
 Example:

21. TYPES OF MATRIX
 Unit/identity:
A square matrix in which all elements are zero
expect diagonal elements are one is called unit
matrix.
It is denoted by “I”.
 Example:
 All matrices shows unit matrix:

22. TYPES OF MATRIX
 Zero/null Matrix:
A matrix in which all elements are zero.
It is denoted by ‘Z’.
 Example:

23. TYPES OF MATRIX
 Transpose of a Matrix:
The interchanging rows and columns the
resulting matrix known as transpose of matrix.
 Example:

24. TYPES OF MATRIX

25. TYPES OF MATRIX
 Symmetric matrix:
If A=A transpose, then matrix
A is called symmetric matrix.
 Example:
 That matrix show symmetric matrix:
 Skew matrix:
If A≠Aˆt, then matrix A is called skew matrix.
 Example:

26. TYPES OF MATRIX
 That matrix show skew matrix

27. TYPES OF MATRIX
 Singular Matrix:
If |A|=0 i.e the value of determinant is zero is
called singular matrix.
 Example:

28. TYPES OF MATRIX
 Non-singular:
If |A|≠0 i.e that is value of determinants not zero is called
Non-singular matrix.
 Example:

29. ADDITION AND SUBTRACTION MATRICES :
 Addition matrix:
In mathematics, matrix addition is the operation
of adding two matrices by adding the
corresponding entries together
 Example:

30. ADDITION AND SUBTRACTION MATRICES :
 Subtraction matrix:
If A and B have the same number of rows and
columns, then:
A - B is defined as A + (-B).
 Example:

31. MULTIPLICATION OF MATRICES
Founder:
 Jacques Philippe Marie Binet (born February 2
1786 in Rennes and died May12 1856 in Paris)
 As the first time the derived the rule for
multiplying matrices in 1812.

32. MULTIPLICATION OF MATRICES
 Definition:
The number of columns of 1st matrix must
be equal to number of rows of 2nd matrix.
 No of columns of 1st matrix=No of rows of 2ndmatrix
.
 Examples:

33. MULTIPLICATION OF MATRICES

34. APPLICATIONS OF MULTIPLICATION
OF MATRICES
Due to recent progress of DNA
microarray technology, a large number
of gene expression profile data are
being produced.
Matrix multiplication is used to analyze
expression in computational molecular
biology.
Matrix is used in this technology to
create simple algorithms

35. APPLICATIONS OF MULTIPLICATION
OF MATRICES

36. APPLICATIONS OF MULTIPLICATION
OF MATRICES
 We can use multiplication matrix to find out the
level of red blood cells in a person.

37. APPLICATIONS OF MULTIPLICATION
OF MATRICES
 Human populations have been increase at a
nearly exponential rate over the last couple of
thousands years.
 Matrix multiplication is used for calculating
population expansion of a species, over a
period of time , provided it grows at a constant
rate. This can be help monitor the population or
over-populated species.

38. APPLICATIONS OF MULTIPLICATION
OF MATRICES

39. MATRICES
 Solve linear equation by using matrix method:
AX=B
Aˆ-1A=Aˆ-1B
IX=Aˆ-1B
X=Aˆ-1B

40. MATRICES
 Find determinant:

41. APPLICATIONS OF MATRICES
 MATRICES IN DIMENSIONAL:
In computer based application, matrices play
a vital rule in the projection of three dimensional
images into two dimensional screens creating the
realistic seeming motions.

42. APPLICATIONS OF MATRICES
 MATRICES IN GOOGLE SEARCH:
Stochastic matrices solver in the page rank
algorithms which are used in the ranking of page
of Google search.

43. APPLICATIONS OF MATRICES
 SEISMIC SURVEYS:
MANY geologists make use certain types of
matrices for seismic surveys. The seismic survey is
one form of geophysical survey that aims at
measuring the earth’s (geo) properties by means of
physical(-physics).
Principles such as:
 Magnetic
 Electric
 Gravitational
 Thermal
 Elastic Theories.

44. APPLICATIONS OF MATRICES
 COMPUTER ANIMATIONS:
Matrix transforms are very useful within the world
of computer graphics software and hardware graphics
processor uses matrices for performing operations
such as:
• Scaling
• Translation
• Reflection
• Rotation

45. APPLICATIONS OF MATRICES
 MATRICES IN CALCULATING :
 Matrices are used in calculating the gross
domestic products in economics which
eventually helps in calculating efficiently.
 Matrices are used in many organizations such
as for scientists for recording their
experiments.
 In engineering, math reports are recorded using
matrices.
 And in architecture, matrices are used with
computing. If needed, it will be very easy to add
the data together, like with matrices in
mathematics.