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8. Consider the set of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of consisting of alldeterminants with values - 1. Then:(a) C is empty(b) Bhas as many elements as c(c) A=BUC(d) B has twice as many elements as c |
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Answer» Option (B) Step-by-step explanation:We know that the interchange of two adjacent rows (or columns ) changes the value of a determinant only in SIGN and not in magnitude. Hence corresponding to EVERY element Δ of B there is an element Δ'in C obtained by interchanging two adjacent rows (or columns )in Δ.It follows that n (B) ≤ n (C). That is, the number of elements in B is less than or equal to the number of elements in C.Similarly, n (C) ≤ n (B).Hence n (B) = n (C), that is B has as many elements as C.Option D is not correct. The set A will also have determinants with values 0. Hence, option C is INCORRECT.Option A is incorrect as C is not empty.Hence, option B is correct.Plsss mark as brainliest |
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