math triangle theory

We have already learnt in the previous class that the area of triangle whose vertices are (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ) is given by Hence area of a triangle having vertices at (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is given by..

Application of Determinants - Now we shall discuss the use of determinants in finding the area of a triangle and in the solution of simultaneous equation..

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..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method etc. They a..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is given by 47.5 sq.units..

(x 1 + x 2 ) + i (y 1 + y 2 ), i.e., z 1 + z 2 . The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only when O, P, Q are ly..

Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is a..

[A i j ] where A i j is the co-factor of the element a i j . Adjoint of A is denoted by Adj A. Note that the concept of adj is only for square matrix. A square matrix A is said to be non-singular if |A| 0. Let A be a square matrix of order n. If there exists a square matrix B of order n, such that ..

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical I..

Mathematical Induction..