Question

8. Consider the set of all determinants of order 3 with entries 0
or 1 only. Let B be the subset of consisting of all
determinants 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​

Answer 1

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.

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