{p E P3 | p(2) = 1}. H = Complete the following statements to determine if H is a subspace of P3. (a) H is ? If it is non-empty, give two different examples of vectors in H. If it is empty, then leave the following spaces blank. example 1: p(x) = example 2: q(x) = Note: Normally, only one example is required to show H is not empty in a proof. (b) H is ? under vector addition. If it is not closed, enter two polynomials p, q E H below, whose sum is not in H. If it is closed, then leave the following spaces blank. p(x) = q(x) = (c) H is ? under scalar multiplication. If it is not closed, enter a scalar k and polynomial r E H below, whose product is not in H. If it is closed, then leave the following spaces blank. k = and r(x) = (d) H ? v of P3.

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