Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be...

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Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be...

Let S = {1 + 3x, 1 − 5x²}. Which of the following polynomials could be added to the set S to form a basis for P₂?

(i) 2 + 3x − 6x²

(ii) 4 + 3x − 16x²

(iii) 9 + 15x − 21x²

(A) all of them (B) (i) and (ii) only (C) (i) and (iii) only (D) (ii) and (iii) only (E) none of them (F) (i) only (G) (ii) only (H) (iii) only

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Answer 1

Answer #1

1-53 Sa (1) 2 32 6zh () q 15X -21x* we need to cheek ohieh of them Ci)i)lii) Cam not be ori Hem as linean combi natin f Suppo ioa basisP 5 4+32-16 1+3 Ci43x) +2 Cl-5 x) = 9+15 x - 2122 Suppose Ci 5 C2 2 1 no Soution 1+3x, 15x, 915x 2.1 x forms abasis if you have any doubt please comment

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Answer 2

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Let S = {1 + 3x, 1 − 5x2}. Which of the following polynomials could be...

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