calculuslover69
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- Sep 28, 2015
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Challenging question in practice test:
Consider the set V of all polynomials with real coefficients - this set is a vector space over R if operations of addition and scalar multiplication are defined
in the “standard” way. (You don’t have to prove that V is a vector space - take it as a given). Consider the subset W of V consisting of all polynomials of degree less or equal to 2. Assume that W also contains 0. Is W a subspace of V? Does the set of vectors in W: {1, x, x + x^2} form a basis of W? What is the dimension of W?
Any ideas?
Consider the set V of all polynomials with real coefficients - this set is a vector space over R if operations of addition and scalar multiplication are defined
in the “standard” way. (You don’t have to prove that V is a vector space - take it as a given). Consider the subset W of V consisting of all polynomials of degree less or equal to 2. Assume that W also contains 0. Is W a subspace of V? Does the set of vectors in W: {1, x, x + x^2} form a basis of W? What is the dimension of W?
Any ideas?
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