Consider the set V of all polynomials with real coefficients...

[calculuslover69]

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?

 

[Deleted member 4993]

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?

What are your thoughts?

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[Ishuda]

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?

What is x+x² times x+x²?