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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..Equality of Matrices
Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...
Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...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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