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Use Theorem 4.2.1 to determine which of the following sets of vectors are subspaces of F(−∞,∞)....

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Advance Math

Use Theorem 4.2.1 to determine which of the following sets ofvectors are subspaces of F(−∞,∞). (Justify!)

(a) The set of all functions f ∈ F(−∞,∞) for which f(0) = 0.

(b) The set of all functions f ∈ F(−∞,∞) for which f(1) = 0.

(c) The set of all functions f ∈ F(−∞,∞) for which f(0) = 1.

(d) The set of all functions f ∈ F(−∞,∞) for which f(−x) = f(x)for all x ∈ R

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