Find a polynomial p(x) of degree at most 2, which is not in the span of...

 

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Find a polynomial p(x) of degree at most 2, which is not in the span of P₁(x) = x² - 2x + 1, P2(z)=1-1, P3 (2) = x² - 1. Are polynomials pi(2), p2(1), P3 (2) of the previous problem linearly independent? Prove it if the answer is yes, or find a non-trivial linear relation (linear dependence) cipi(x) + c₂p2(x) + C3P3 (2) = 0, C₁, C2, C3 ER if the answer is no. Find a polynomial p(x) of degree at most 2, which is not in the span of P₁(x) = x² - 2x + 1, P2(z)=1-1, P3 (2) = x² - 1. Are polynomials pi(2), p2(1), P3 (2) of the previous problem linearly independent? Prove it if the answer is yes, or find a non-trivial linear relation (linear dependence) cipi(x) + c₂p2(x) + C3P3 (2) = 0, C₁, C2, C3 ER if the answer is no.

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