3. Let P2(R) be a vector space (over the field of real numbers) of polynomials p (t) of the degree not exceeding 2 with real-valued coefficients. Give an example of a basis of P2 (R). Find out if the following set of polynomials {2t? +t+ 1, –3t²+ 2t + 1, –9t² – t – 2} is a basis of P2 (R).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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3. Let P2(R) be a vector space (over the field of real numbers) of polynomials p (t) of
the degree not exceeding 2 with real-valued coefficients. Give an example of a basis of
P2 (R). Find out if the following set of polynomials
{2t? +t+1, –3t? + 2t + 1, –9t² –t – 2}
is a basis of P2 (R).
Transcribed Image Text:3. Let P2(R) be a vector space (over the field of real numbers) of polynomials p (t) of the degree not exceeding 2 with real-valued coefficients. Give an example of a basis of P2 (R). Find out if the following set of polynomials {2t? +t+1, –3t? + 2t + 1, –9t² –t – 2} is a basis of P2 (R).
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