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6 Nov 2019
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Decide whether each set forms a vector space under the usual operations of addition and scalar multiplication. If the set does form a vector space, give a brief proof; if not, explain why not. (Use the Subspace Lemma 2.9 if possible.) The diagonal matrices A = { |x, y epsilon R}. B = { |x, y epsilon R} C = {(x, y, z, w) | x, y, z,w epsilon R and x + y + w = 3}. The set of function D = {f: R rightarrow R | df/dx + 2f = 0}. E = {f: R rightarrow R} | f(7) = 0}. F = {f: R rightarrow R | degree (f) 2 or f(x) equiv 0} . we write f(x) equiv 0 for the zero function defined by f(x) = 0 for all x. Show transcribed image text
Show all steps.
Decide whether each set forms a vector space under the usual operations of addition and scalar multiplication. If the set does form a vector space, give a brief proof; if not, explain why not. (Use the Subspace Lemma 2.9 if possible.) The diagonal matrices A = { |x, y epsilon R}. B = { |x, y epsilon R} C = {(x, y, z, w) | x, y, z,w epsilon R and x + y + w = 3}. The set of function D = {f: R rightarrow R | df/dx + 2f = 0}. E = {f: R rightarrow R} | f(7) = 0}. F = {f: R rightarrow R | degree (f) 2 or f(x) equiv 0} . we write f(x) equiv 0 for the zero function defined by f(x) = 0 for all x.
Show transcribed image text