Let P3 be the vector space of polynomials up to degree 3. This means that a...

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Let P3 be the vector space of polynomials up to degree 3. This means that a vector in P3 looks like this: p(x) = ao + a + ax where the values of a; can be any real number. Consider the set of vectors: P(x) = 1 + x P2(x) = x(x - 1) P3(x) = 1 + 2x Prove this set of vectors is a basis for P3 by showing two properties: 1) The set is linearly independent. 2) The set of vectors spans P Let P3 be the vector space of polynomials up to degree 3. This means that a vector in P3 looks like this: p(x) = ao + a + ax where the values of a; can be any real number. Consider the set of vectors: P(x) = 1 + x P2(x) = x(x - 1) P3(x) = 1 + 2x Prove this set of vectors is a basis for P3 by showing two properties: 1) The set is linearly independent. 2) The set of vectors spans P

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