 so, ame matrix are vivinna pokar bhi kaya alasana kailo ita ame matrix are vivinna operasana bhi kaya alasana kailo to yate muthote tinita operasana se addition and subtraction of 2 matrices and multiplication of 2 matrices so, ame ita operasana on matrix are bhi kaya alasana kailo so, basic operation on matrices are first addition and subtraction of 2 matrices number 2 multiplication of a matrix by scalar number 3 ame alasana kailo multiplication of 2 matrices so, itinita ame basic operation on matrix are addition and subtraction of 2 matrices multiplication of a matrix by scalar and multiplication of 2 matrices ita ame yate yate ame alasana kailo so, first ame alasana kailo addition of and subtraction of 2 matrices so, jodhi ame duta matrix soilo a n b if a n b are 2 matrices of same order so, jodhi ame duta matrix same order duta matrix thorough then their sum is denoted by a plus b so, matrix duta sum above a plus b is again a matrix of same order is again a matrix of same order obtained by adding the corresponding elements of elements of a n b thick thena kailo ame similarly subtraction duta matrix of subtraction a minus b is defined as a minus b ame defined kailo paro ane kailo a minus b equal to a plus minus 1 bracket b so, ita ame subtraction form so, duta matrix or ame addition is denoted by a plus b n is obtained by adding the corresponding elements of a n b a subtraction is denoted by a minus b or a 2 ame defined kailo a minus b equal to a plus bracket minus 1 into b ita ame duta yodhanlom jodhan under ame duta matrix or addition or subtraction to ame already ame defined kailo paro so, dhara hall ame duta matrix ame dhori sum same order 1 2 minus 1 3 2 1 2 into 3 and b so, duta matrix ame dhailo a and b of the same order 2 by 3 so, ame ita addition addition to ame defined kailo a plus b so, ame duta matrix addition ame obtained by adding corresponding elements of a and b 1 plus 4 8 kailo 2 plus 2 minus 1 plus 4 3 plus 2 2 plus 3 1 plus 6 so, ame corresponding elements for 8 kailo ita ame is to result paro ita result to about 5 4 3 3 plus 2 5 5 7 so, ame ita extra coming addition of a and b will come or ame ita extra order to ame come 2 by 3 so, now we find subtraction of a and b subtraction a minus b so, a minus b so, a is 1 2 minus 1 3 2 1 minus 4 2 4 2 3 6 so, now we get subtracting corresponding elements of a and b so, 1 minus 4 is minus 3 2 minus 2 0 minus 1 minus 4 minus 5 3 minus 2 1 2 minus 3 minus 1 1 minus 3 minus 5 so, this is the subtraction of a and b so, this matrix also ordered 2 by 3 so, ame operation multiplication of a matrix by a scalar multiplication of a matrix by a scalar so, ame ita matrix ame geta a so, ame ita matrix a of order 2 by 3 so, ame matrix so, ame ita scalar so, ame ita scalar so, k is a scalar k is a scalar so, ame matrix multiply so, ame result to pump kb kc Kd Ke Kef so, ame ita matrix of a scalar multiply ame geta geta elementary a a scalar multiply to order of 2 by 3. Next, I will multiply two matrices. A matrix A is said to be conformable for multiplication with a matrix B if the number of columns of A is equal to the number of row of B. So, at a matrix, I will multiply B by 3 conformable for matrix. So, the number of columns of A is equal to the number of row of B. So, A short to shorty, the bottom matrix or number of column is equal to the number of row of second matrix. That is, I mean I will multiply the problem. A equal to A11, A12, A21, A22, A31, A32. So, in a matrix A, I will order from 3 by 2 and B11, B12, B21, B22 order 2 by 2. So, I mean matrix A, we can multiply with matrix B because here number of column is 2 and number of row of B is 2. So, here condition is satisfied. Number of column of A is equal to the number of row of B. So, we can multiply A and B. So, now we get AB. So, AB we get first we multiply this row with this column. So, we get A11, B11 plus A12, B21. Next we multiply this row with this column. So, we get A11, B12, A plus A12, B22. So, next with this row we multiply this column. So, A21, B11 plus A22, B21, A21, B12 plus A22, B22. So, last row will be multiply this row with this column A31, B11, A32, B21. So, last remain will be multiply this row with this column. So, we get A32, B12 plus A32, B22. So, this is the multiplication of these two matrix A and B. So, we get AB. So, order of this matrix will be 3 by 2. So, this way we can multiply two matrix. If there is a condition that should be satisfied that condition is number of column of A is equal to the number of row of B. So, now we discuss transpose of a matrix. So, transpose of a matrix is obtained by interchanging rows and columns of A and it is denoted by A dash. And for example, if we consider a matrix A equal to 205, 124, an order of this matrix is 2 by 3 and transpose of this matrix is obtained by interchanging row and columns of this. So, after interchanging row and columns we get this row becomes column 205 and this row becomes column we get this. So, order of this matrix will be 3 by 2. So, this is called transpose of this matrix. So, now we discuss some properties of transpose of a matrix. So, number one properties, if A is a matrix then we get transpose of a transpose is the matrix A, original matrix A. If we take two transpose of a matrix then we get the original matrix. Then if A is a matrix of order m by n and k is a scalar then we get k A whole transpose equal to k into transpose. So, next properties if A and B are two matrices then two matrices of same order then A plus B whole transpose equal to A transpose plus B transpose. So, next number of four properties if A and B are two matrices conformable for multiplication then we get A B whole transpose equal to B transpose into A transpose. So, these are the four properties of a transpose of a matrix. So, last we define two important matrix. So, these two matrix are symmetric matrix, symmetric matrix and square symmetric matrix. So, first we define symmetric matrix. So, a square matrix A is said to be symmetric if A transpose equal to A. So, square matrix A is said to be symmetric if we take a transpose of a matrix we get the same matrix. So, for example suppose A is a matrix the elements are 6 3 minus 6 9 minus 6 8 5 9 5 2. So, if we take transpose of this matrix 3 minus 6 9 minus 6 8 5 9 5 2. So, we get same matrix A. So, this is the same. So, this is called a symmetric matrix. So, next we define a square symmetric matrix, a square symmetric matrix. So, next we define a square symmetric matrix. A square matrix A is said to be a square symmetric A transpose equal to minus A. For example, if we take a matrix A. So, elements are 0 3 2 3 minus 2 0 4 minus 3 minus 4 0. So, we if we take transpose we get 0 2 3 minus 2 0 4 minus 3 minus 3 minus 4 0. So, this is a square symmetric matrix because if we take here minus common then we get. So, this is the matrix A minus A. So, therefore, A transpose equal to minus A. So, therefore, this matrix is a square symmetric matrix. So, today class we discuss unit 5 of course 1 classical algebra and trigonometry. So, unit 5 is matrices. Here we discuss above matrices. First we define what is matrix. Then we discuss there are different types of matrix. Then we get 3 basic operation on matrix A. So, this is matrix A. So, that operation are addition and subtraction of 2 matrices, multiplication of a matrix by a scalar and multiplication of 2 matrices. And last we discuss transpose of a matrix and their properties. And here we define 2 important matrix symmetric matrix and square symmetric matrix. So, this is the all about this unit 5 matrices matrix. So, there are also there are some more points. So, we will discuss this points in next class. Thank you.