Area of a Triangle
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..
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 Matrices and Determinants
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..
Conclusion
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 fi..
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 method etc. They a..
Question 10
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle,..
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle,..Summary
[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 ..
[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 ..Some Observations
The binomial coefficients in (a + b) n , which are equidistant from beginning and end are equal. The binomial coefficients in the expansion of (a + b) n can be easily evaluated by using the Pascal's triangle given below: In the Pascal's triangle, each row sta..
The binomial coefficients in (a + b) n , which are equidistant from beginning and end are equal. The binomial coefficients in the expansion of (a + b) n can be easily evaluated by using the Pascal's triangle given below: In the Pascal's triangle, each row sta..Binomial Theorem Summary
>Here, a and b may be any numbers. Pascal's triangle The coefficients of various terms in (a+b) n for different values of n follows the pattern given below: General term For 0 < r < n, T r+1 in the expression of (a + b) n is given by T r+1 = n C r a n-r b r . (r + 1) t h t..
>Here, a and b may be any numbers. Pascal's triangle The coefficients of various terms in (a+b) n for different values of n follows the pattern given below: General term For 0 < r < n, T r+1 in the expression of (a + b) n is given by T r+1 = n C r a n-r b r . (r + 1) t h t..Triangle
A three sided closed figure is called a triangle. Here side means a line segment. ABC is a triangle. BC, CA, AB are its sides. They can be denoted by small letters a, b and c. The capital letters A, B and C denote the vertices of the triangle..
A three sided closed figure is called a triangle. Here side means a line segment. ABC is a triangle. BC, CA, AB are its sides. They can be denoted by small letters a, b and c. The capital letters A, B and C denote the vertices of the triangle..Triangle
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