Determine whether the following are subspaces of P4 (be careful!): The set of polynomials in P4 of even degree

Find the dimension of the subspace Hof R2 spanned by

5. Let p(x) be a polynomial in P4. Let S be the set of all polynomials from P4 with p(0) = 0. Is S a subspace of P4? Why or why not?

Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 14x² + 12x +11, 9x² + 8x +7 and - (22x² + 20x +17). a. The dimension of the subspace His b. Is {14x² + 12x + 11, 9x² + 8x +7, − (22x² + 20x +17)} a basis for P₂? choose c. A basis for the subspace H is { Be sure you can explain and justify your answer. }. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of ².

Given 7: = -10] -7 2 [0] -3 - find the closest point to in the subspace W spanned by 1-0 and