GOVT. COLLEGE ROPAR DAPARTMENT OF ECONOMICS

Transcript:GOVT. COLLEGE ROPAR DAPARTMENT OF ECONOMICS:
GOVT. COLLEGE ROPAR DAPARTMENT OF ECONOMICS TOPIC-: MATRICES INTRODUCTION DEFINITION TYPE OF MATRICES PROF. RITU CLASS– B.A3 SEM6 INTRODUCTION-: Modern system dynamics is based upon a matrix representation of the dynamic equations governing the system behavior. A basic understanding of elementary matrix algebra is essential for the analysis of state-space formulated systems. A full discussion of linear algebra is beyond the scope of this note and only a brief summary is presented here. The reader is referred to a text on linear algebra, such as Strang (1980), for a detailed explanation and expansion of the material summarized here. DEFINITION OF MATRICES-: e.g-: TYPE OF MATRICES-: There are some of the important types of matrices that are used in mathematics, engineering, and science. Here is the list of the most commonly used types of matrices in linear algebra: Row Matrix Column Matrix Scalar matrix Rectangular Matrix Square Matrix Identity Matrices Zero Matrix Diagonal Matrix We can use these different types of matrices to organize data by age group, person, company, month, and so on. We can then use this information to make decisions and solve a lot of math problems. 1. ROW MATRIX-: A matrix of an order m x n, where m is the number of rows and n is the number of columns, is a row matrix, if and only if, m = 1. Hence, a matrix of the order of 1 x n is a row matrix. The horizontal lines of elements form a row matrix. 2. COLUMN MATRIX-: A column matrix is a type of matrix that has only one column. The order of the column matrix is represented by m x 1, thus the rows will have single elements, arranged in a way that they represent a column of elements. Row and column in a matrix hold the elements. The row elements are horizontally arranged and column elements are vertically arranged. Unlike a column matrix, a row matrix will have a single row only. 3.SACLAR MATRIX-: The scalar matrix is a square matrix having a constant value as every element of its principal diagonal, and all other elements are equal to zero. The scalar matrix is a square matrix having an equal number of rows and columns 4.RECTANGULAR MATRIX-: Rectangular matrix is one type of matrix. In this matrix, the elements are arranged in rows and columns. The arrangement of elements in the matrix represents a