mathematics for class x triangles%5d

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 , ..

[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 ..

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

Question: Find the number of triangles that can be drawn through 12 distinct points, no three of which are collinear. Answer: To draw a triangle, we require three non-collinear points. Hence, the number of triangles that can be drawn 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..

1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..

Conclusion - 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 metho..

Solve the system of linear equations. x +2y + 3z = 6 2x + 4y + z = 7 3x + 2y + 9z = 14 using Cramer's rul..

If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and ..

Number of ways of filling hundred's place = 2 Number of ways of filling ten's place = 2 Number of ways of filling unit's place = 2 By the fundamental principle of counting, the total number of numbers = 2 x 2 x 2 =..