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Let P11(x) be the real vector space of polynomials, in the variable x with real coefficients and having degree at most 11, together with the zero polynomial. Let
E = {s0(x), s1(π₯), β¦ , s11(x)}, F = {r0 (x), r1 (x), β¦ , r11(x)}
be subsets of P11(x) having 12 elements each and satisfying
s0 (3) = s1 (3) = β― = s11(3) = 0 , r0(4) = r1(4) = β― = r11(4) = 1.
Then, which one of the following is TRUE ?
Let P11(x) be the real vector space of polynomials, in the variable x with real coefficients and having degree at most 11, together with the zero polynomial. Let
E = {s0(x), s1(π₯), β¦ , s11(x)}, F = {r0 (x), r1 (x), β¦ , r11(x)}
be subsets of P11(x) having 12 elements each and satisfying
s0 (3) = s1 (3) = β― = s11(3) = 0 , r0(4) = r1(4) = β― = r11(4) = 1.
Then, which one of the following is TRUE ?
E = {s0(x), s1(π₯), β¦ , s11(x)}, F = {r0 (x), r1 (x), β¦ , r11(x)}
be subsets of P11(x) having 12 elements each and satisfying
s0 (3) = s1 (3) = β― = s11(3) = 0 , r0(4) = r1(4) = β― = r11(4) = 1.
Then, which one of the following is TRUE ?
Updated On: Oct 1, 2024
- Any such E is not necessarily linearly dependent and any such F is not necessarily linearly dependent
- Any such E is necessarily linearly dependent but any such F is not necessarily linearly dependent
- Any such E is not necessarily linearly dependent but any such F is necessarily linearly dependent
- Any such E is necessarily linearly dependent and any such F is necessarily linearly dependent
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The Correct Option is B
Solution and Explanation
The correct option is (B) : Any such E is necessarily linearly dependent but any such F is not necessarily linearly dependent.
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