Study guides, Class notes & Summaries

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 ...

Wolczuk Linear Algebra Solutions Latest 2021

A study of Greco-Roman mythology and legend, with special emphasis on the Olympian gods and the figure of the hero. Topics may include myths of creation, the rise of the gods, divine myths, the tales surrounding the cities of Troy, Mycenae, and Thebes and the heroes Herakles, Perseus, and Theseus.