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University of Waterloo MATH 136 Assignment 7 Solutions
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July 2021

2020/2021

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University of Waterloo MATH 136 Assignment 7 Solutions 1. Determine, with proof, which of the following are subspaces of the given vector space: (a) S1 = {p(x) ∈ P4(R) | p(1) = 0} of P4(R). Solution: By definition, S1 is a subset of P4(R) and z(x) = 0 ∈ S1 since z(1) = 0. Thus, S1 is a non-empty subset of P4(R). Let p(x), q(x) ∈ S1. Then p(1) = q(1) = 0. Hence, (p + q)(1) = p(1) + q(1) = 0 + 0 = 0, and so (p + q)(x) ∈ S1. Now, let t ∈ R, then (tp)(1) = t(p(1)) = t(0) = 0, and ...
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