Project business maths
- 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.
- 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:
- 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
- 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.