Question:
Let V be the real vector space consisting of all polynomials in one variable with real coefficients and having degree at most 5, together with the zero polynomial. Let T: V→ \(\R\) be the linear map defined by 7(1) = 1 and T(x(x-1)... (x-k+1)) = 1 for 1 ≤ k ≤ 5.
Then which of the following is/are true?
Let V be the real vector space consisting of all polynomials in one variable with real coefficients and having degree at most 5, together with the zero polynomial. Let T: V→ \(\R\) be the linear map defined by 7(1) = 1 and T(x(x-1)... (x-k+1)) = 1 for 1 ≤ k ≤ 5.
Then which of the following is/are true?
Then which of the following is/are true?
Updated On: Oct 1, 2024
- T(x4) = 15.
- T(x3) = 15.
- T(x4) = 14.
- T(x3) = 3.
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The Correct Option is A, B
Solution and Explanation
The correct option is (A): T(x4) = 15. and (B): T(x3) = 15.
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