k 1 math games

If D = 0 and all D 1 , D 2 and D 3 are zeros, this system has either infinite solution or no solution. In this case, put x = k(y = k or z = k), in any two of the equations, find y and z in terms of k. Substitute these values of x, y and z in term..

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..

1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+..

The system of linear equations may be expressed as AX = B. Step 2: Find |A|. If |A| 0, the system has unique solution which is given by X = A - 1 B. Step 3: If |A| = 0, put x = k (y = k or z = k) in any two of the given equations and find y and z in terms of ..

\ n = ..

If we put r = n in the above formula, the..

Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done in ..

Only a square matrix can have its invers..

C(n,r) = C(n,n-..

Consider the GP a, ar, ar 2 ... ..