discrete mathematics

Let |aij| be a determinant of order n. The determinant obtained by deleting the i t h row and j t h column in which the element a i j lies is called the minor of element a i j and is denoted by M i ..

If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) times th..

Row Matrix, Column Matrix, Square Matrix, Diagonal Matrix, Scalar Matrix, Identity or Unit Matrix, Null Matrix or Zero Matr..

Let A = [aij] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is ..

Application of Determinants, Area of a Triangle, Cramer's rule for the solution of a system of equations in 2 variables, Consistency of a system of linear equation. Application of Matrices, Homogeneous Equations (Constant = 0), Non Homogenous Equations (Solution by the Matrix Metho..

In this chapter, we have seen how arranging numbers in orderly rows and columns under the guise of Matrices and Determinants, has helped to solve linear equations or find the area of a triangle. There are in fact other much wider applications in Science and Engineering and other fields...

>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addition A(B + C) = AB + AC or (A +..

A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital lette..

Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...

If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..