Let H be the set of polynomials (a) Give two different examples of polynomials in H....

    

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Let H be the set of polynomials (a) Give two different examples of polynomials in H. example 1: p(x) = example 2: q(x) = (b) Give two different examples of polynomials from P3 which are not in H. example 1: p(x) = example 2: q(x) = (c) Complete the following statements to determine if H is a subspace of P3. 0 ? ✓in H. q(x) = His ? ✓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) = k= = {p = P₂ | p(2) = 0}. His ? ✓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. and r(x) = H? H = ✓of P3. (c) Complete the following statements to determine if H is a subspace of P3. 0? His ✓? If it is p(x) q(x) = = ✓in H. closed NOT closed under vector addition. No polynomials p, q E H below, whose sum is not in H. H is ✓? If it is k = H ? closed NOT closed and r(x) = under scalar multiplication. scalar k and polynomial r E H below, whose product is not in H. ✓ of P3. His ? under scalar multiplication. If it is not closed, enter a scalar k and polynomial r E H below, whose product is not in H. and r(x) k = H✓? is a subspace is not a subspace of P3. Let H be the set of polynomials (a) Give two different examples of polynomials in H. example 1: p(x) = example 2: q(x) = (b) Give two different examples of polynomials from P3 which are not in H. example 1: p(x) = example 2: q(x) = (c) Complete the following statements to determine if H is a subspace of P3. 0 ? ✓in H. q(x) = His ? ✓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) = k= = {p = P₂ | p(2) = 0}. His ? ✓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. and r(x) = H? H = ✓of P3. (c) Complete the following statements to determine if H is a subspace of P3. 0? His ✓? If it is p(x) q(x) = = ✓in H. closed NOT closed under vector addition. No polynomials p, q E H below, whose sum is not in H. H is ✓? If it is k = H ? closed NOT closed and r(x) = under scalar multiplication. scalar k and polynomial r E H below, whose product is not in H. ✓ of P3. His ? under scalar multiplication. If it is not closed, enter a scalar k and polynomial r E H below, whose product is not in H. and r(x) k = H✓? is a subspace is not a subspace of P3.

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a Two polynomials be px q x as we c d qx x2 then So ... View the full answer