TS EAMCET · Maths · Determinants
Let \(A\) be the set of all \(3 \times 3\) determinants with entries 0 or 1 only and \(B\) be the subset of \(A\) consisting of all determinants with value 1 . If \(C\) is the subset of \(A\) consisting of all determinants with value -1 , then
- A \(n(C)=0\)
- B \(n(B)=n(C)\)
- C \(A=B \cup C\)
- D \(n(B)=2 n(A)\)
Answer & Solution
Correct Answer
(B) \(n(B)=n(C)\)
Step-by-step Solution
Detailed explanation
We know that the interchange of two adjacent rows (columns) changes the value of a determinant only in sign but not in magnitude. Hence, corresponding to every element \(\Delta\) at \(B\) there is an element \(\Delta^{\prime}\) in \(C\) obtained by inter changing two adjacent…
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