problem solving in math more:label problem 20solving 20in 20math more:math

Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life scienc..

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-Jorda..

Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life science..

Using matrix method solve the following systems of linear equations 2x - y + z = -3 3x - z = - 8 2x + 6y ..

Using matrix method, solve the following system of linear equations x + y + z = 6 (1) x + 2y + 3z = 14 (2) x + 4y + 7z = 30 ..

= (14 - 12) - (7 - 3) + (4 - 2) = 2 - 4 + 2 = 0 The system may have infinite number of solutions or no solution. Put x = k in (1) and (2) and solve y + z = 6 - k 2y + 3z = 14 - k. Solving the above two equations, we have z = k + 2 and y = 4 - 2k When x = k, substituting t..

If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and the second equation ..

[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 ..

Question: Prove that following lines are concurrent: 15x - 18y + 1 = 0, 12x + 10y - 3 = 0, 6x + 66y - 11 = 0. Answer: 15x - 18y + 1 = 0 ...(i) 12x + 10y - 3 = 0 ...(ii) 6x + 66y - 11 = 0 ...(iii) Solve (i) and (ii) for x and y, ..

Question 1 - Question: Find the centroid of the triangle whose sides are x + y - 1 = 0, x - 3y + 3 = 0 and x - y - 1 = 0. Answer: Let AB represent the side x + y - 1 = 0 ...(i) Let BC represent the side x - 3y + 3 = 0 ... (ii) Let CA represent the side x - y - 1 = 0 ... (iii) Solving (i) ..