 Hi, and welcome to the session. Today we will learn about matrices. First of all, let us see what is a matrix? A matrix is an ordered rectangular numbers functions. For example, this is a matrix and we denote matrices by capital letters say A. Now these numbers or the functions are called the elements or entries of the matrix. Also the horizontal lines of elements are called the rows of the matrix and the vertical lines of elements are called the columns of the matrix. Now let's see what is the order of a matrix? A matrix columns is called a matrix of order m by n. Here in this matrix there are two rows and three columns. So the order of this matrix is 2 by 3. Now by looking at the order of the matrix we can say that how many elements will be there in the matrix. So here the order of the matrix is 2 by 3 and 2 into 3 is 6. So there are six elements in this matrix. Now this is the general form of a matrix of order m by n in which there are m rows and n columns. The general element of this matrix is denoted by aij where this is the element of ith row and jth column. And we denote the matrix by aij of order m by n. Now let's move on to types of matrices. Here we have column matrix. The matrix is the matrix which has only one column. The general notation for a column matrix is aij of order m by 1. That means there are m rows and only one column. For example this is a column matrix of order 4 by 1. That is there are four rows and only one column. Now next we have row matrix. Row matrix is a matrix which has only one row. The general notation of a row matrix is aij of order 1 by n. That means there is only one row and n columns. For example this is a row matrix of order 1 by 3. Next is a square matrix. A matrix is a matrix in which number of rows is equal to number of columns. Here this is a square matrix of order 3 by 3. That means number of rows is equal to number of columns. In general a given as aij of order m by m is a square matrix order m. In a square matrix say this one. Elements a, q and z constitute the diagonal of matrix a. So these are the diagonal elements of matrix a. Let us see what is a diagonal matrix? A square matrix non-diagonal elements 0 is called the diagonal matrix. For example if all the elements except these diagonal elements are 0 then this is a diagonal matrix. In general a matrix a given by aij of order m by m is a diagonal matrix aij is equal to 0 when i is not equal to j. Now let us see what is a scalar matrix? A diagonal matrix all diagonal elements are equal is called a scalar matrix. For example in this diagonal matrix all the diagonal elements are equal to 2.5. So it is a scalar matrix. After this we have identity matrix. A square matrix in which diagonal elements equal to 1 diagonal elements are equal to 0 is called a identity matrix. For example these both are identity matrices. A is an identity matrix of order 3 and B is an identity matrix of order 2. Lastly we have zero matrix and this is also known as null matrix. All elements equal to 0 is called a zero matrix. For example a is a zero matrix over here. Now let us move on to the next topic that is equality of matrices. Two matrices say a given as aij and b given as bij equal they are of same order each element a is equal to the corresponding that is aij is equal to bij for all i and j. For example these both matrices are equal as they both are of order 2 and the elements of first matrix are equal to the corresponding elements of the second matrix. So with this we finished this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.