What is the coefficient of x2 in (1 + x)11? Describe how relation can be represented using matrix.

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Suresh Chand · Accepted Answer

Solution: In Short: 11C2 = (frac{11!}{2! times (11 - 2)!}) = 55 Explanation: In the example of (a + b)n, the (r + 1)th term, denoted by tr + 1, is given by tr + 1 = nCr . an-r . br Letting a = 1, b = x and n = 11, we get tr + 1 = 11Cr . 111-r . xr As, we need the cofficient of x2, we have to take r = 2 11C2 = (frac{11!}{2! times (11 - 2)!}) = 55 The coefficient of x2 in (1 + x)11 is 55. Representaton of Relation using Matrix: Let A = {a1, a2, ........, am} and B = {b1, b2, ........., bn) are finite sets containing m and n elements respectively and set R be a relation from A to B then R can be represented by the mn matrix. MR = [mij] where mij = (left{begin{matrix}1 enspace if enspace (a_i, b_j) enspace ∈ enspace R  0 enspace if enspace (a_i, b_j) enspace ∉ enspace Rend{matrix}right.) The matrix MR is called matrix of R. Example: Let A = {1, 3, 4}, R = {(1, 1), (1, 3), (3, 3), (4, 4)} MR = (begin{bmatrix}1 & 1 & 0 0 & 1& 0 0 & 0 & 1end{bmatrix})

What is the coefficient of x² in (1 + x)¹¹? Describe how relation can be represented using matrix.

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What is the coefficient of x2 in (1 + x)11? Describe how relation can be represented using matrix.

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What is the coefficient of x² in (1 + x)¹¹? Describe how relation can be represented using matrix.