WELCOME TO THE HIGHER MATHEMATICS CLASS SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE scnctg@gmail.com

MATRIX Today`s Topics is Chapter - 1 Exercise -1(A) Book: Higher Mathematics Axorpotra Publications

Learning Outcomes After complete this chapter students can 1.Definition of Matrix 2. Explain Different Types of Matrices

Let us consider the following system of equations X+2y+3z=11 2x-y-z=-3 3x+4y+2z=17 If we arrange the coefficients of x,y,z in the order in which they occur in the given equations and enclose them in brackets. We get the following rectangular array of numbers

Definition of Matrix: Matrix is a rectangular array of real or complex numbers in rows and columns. It is denoted by A,B,C etc. Definition of Rows: The Horizontal Lines of a Matrix are called Rows. Definition of Columns: The Vertical Lines of a Matrix are called Columns. If there are m rows and n columns in the matrix, then the matrix is called a mn matrix(m by n) Order of a Matrix: The numbers of Rows and Columns is called Order of a Matrix .

Different types of Matrices: 1.Square Matrix: A Matrix having equal number of rows and columns is called a Square matrix. If the Matrix A has n rows and n columns it is said to be a Square Matrix of order n. Example: is a Square matrix of order 3.

2.Horizontal Matrix: A matrix mn is called a Horizontal if m<n Example: A= 3. Vertical Matrix: A matrix mn is called a Vertical if m>n

4.Column Matrix : A Matrix having only one column is called a column matrix. Example: A= 5.Row Matrix:A Matrix having only one row is called a row matrix. Example : A=[1 2 3]

6.Zero Matrix : A Matrix whose all the entries are zero is called zero Matrix or null matrix. Example: 0= 7. Diagonal Matrix : A square Matrix having all the entries not occurring along the Principal diagonal equal to zero( at least 1 entry is non zero at principal diagonal) is called a diagonal Matrix. Example A= B=

8.Scalar Matrix: A Square Matrix is said to be a Scalar Matrix if all the Entries along the Principal diagonal are equal and all entries not occurring along the Principal diagonal are zero. Example A= 9.Identity Matrix: A Square Matrix is said to be a Identity Matrix if all the Entries along the Principal diagonal are unity(1)and all entries not occurring along the Principal diagonal are zero. Example I=

EVALUATION Tell me the Definition of Matrix What is Square Matrix?

Learn Different types Matrix HOME WORK Learn Different types Matrix

THANKS TO ALL, DEAR STUDENT Sir Issac Newton, Father of Calculus