Matrices

Matrices

1. MATRICES NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS https://www.slideshare.net/NadeemUddin17 https://nadeemstats.wordpress.com/listofbooks/

2. Introduction:   The idea of matrices was introduced by a famous mathematician Arther Kally in 1857. Matrices is a subject that has wide application in the field of mathematics.   A matrix is a square/rectangular array of numbers written within square brackets in a definite order, in rows and columns.

3. Order of a Matrix   If there are ‘r’ rows and ‘c’ columns in a matrix A, then the order of the matrix is r x c. Order of matrix A is 2 x 2

4. Types of matrices (1)Rectangular Matrix If the number of rows and number of columns in a matrix are not equal the matrix is called a rectangular matrix. For e.g , ,

5. (2)Column Matrix If a matrix has only one column, it is called a column matrix or column vector. For e.g , ,

6. (3)Row Matrix If a matrix has only one row, it is called a row matrix or row vector. For e.g , (4) Square Matrix If the number of rows and columns in a matrix are equal, the matrix is called square matrix. For e.g ,

7. (5) Diagonal Matrix A square matrix with all its elements zero, except elements in the leading diagonal, is called a diagonal matrix. For e.g , , ,

8. (6) Scalar Matrix A diagonal matrix, all whose leading diagonal elements are equal is called a scalar matrix. For e.g , , ,

9. (7) Null matrix OR Zero Matrix A matrix all of whose elements are zero, is called a null matrix. For e.g , , ,  

10. (8) Unit Matrix A diagonal matrix in which the leading diagonal elements equal 1 is called a unit or identity matrix. A unit matrix is denoted by the symbol ‘I’. For e.g ,