Matrices L N

Matrices Matrix -A matrix (plural matrices) is a rectangular array of rows and columns of elements. The elements may be number or things. Matrices are usually denoted by capital letters. The following are some examples of matrices. The Order of Matrix A matrix having m rows and n columns is called a matrix of order m X n (read as “m by n”) Types of matrices i. Row matrix -A matrix with only one row and any number of columns is called row matrix. For example, [3, 0, 1] is a row matrix of order 1 X 3 and [2] is a row matrix of order 1 X 1. ii. Column matrix -A matrix with only one column and any number of rows is called a column matrix for example, is a column matrix of order 3 X 1 and [2] is a column matrix of order 1 X 1. Here we see that [2] is both a row matrix as well as a column matrix. iii. Zero matrix -A matrix with all zero element is called a zero matrix or null matrix. iv. Square matrix -A matrix with same number of rows and columns is called a square matrix. v. Diagonal matrix -A square matrix having elements in main diagonal only and the other element are zero.vi. Scalar matrix -A square matrix whose all diagonal elements are equal and non diagonal elements are zero. vii. Identity matrix -A square matrix whose non -diagonal elements are zero and diagonal elements are 1 Equality of matrices : -Two matrices are said to be equal if they are of same order and their corresponding elements are equal. then a = 1, b = 3, c = 6, d = 2, e = 4, f = 5. Multiple of a matrix by a scalar : -When a matrix is multiplied by a scalar then all the elements of the matrix are multiple by the same scalar. For example if Also, i. K (A + B) = KA + KB ii. (K + K’) A = KA + K’ A Addition of two matrices : -Two or more matrices of same order can be added. For example i. A + B = B + A ii. A + (B + C) = (A + B) + C Multiplication of matrices : -The product of matrices A and B exists if order of A is m X n and order of B is n X p. Then order of the product AB is m X p.i. ii. If AB = 0 A = O or B = O or both A and B are zero iii. If AB = AC, where then it is not necessary that B = C. iv. A(BC) = (AB)C v. If A and I have same order then A I = IA = A vi. Let A be a matrix and B be a null matrix of the same order as A then AB = BA = O. Transpose of Matrix : -The matrix obtained by interchanging the rows and column of a matrix is called the transpose of the matrix. then transpose of A denoted by ample -1. Solution : Example -2.Solution : Example -3. Solution : Examples -4. Solution : Example -5.Solution : Example -6. Solution :