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The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 1 = 6, A 2 2 = -2, A 2 3 = -14 A 3 1 = 1, A 3 2 = 5, A 3 3 = 3 ..
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 1 = 6, A 2 2 = -2, A 2 3 = -14 A 3 1 = 1, A 3 2 = 5, A 3 3 = 3 ..Addition of Matrices
If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..
If A and B are 2 matrices of the same order, then A + B is the sum of the 2 matrices where each element is got by adding corresponding elements of A and B. ..Verification by numerical problems
then show that (A+B)+C = A+(B..
then show that (A+B)+C = A+(B..Suggested answer:
We have 3A - 2B = 3A+(-2)..
We have 3A - 2B = 3A+(-2)..Example:
The matrices are scalar matrices of order 2 and 3 respectivel..
The matrices are scalar matrices of order 2 and 3 respectivel..Suggested answer:
We are to select 4 students from 32. This selection can done i..
We are to select 4 students from 32. This selection can done i..Proof:
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s...
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s...Examples:
8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..
8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..Corollary 1:
If we put r = n in the above formula, the..
If we put r = n in the above formula, the..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..See what our Users say :
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