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Let a ∈ R. Show that {e^ax, xe^ax} is a linearly independent subset of the vector...

Let a ∈ R. Show that {e^ax, xe^ax} is a linearly independent subset of the vector space C[0, 1].

Let a, b ∈ R be such that a≠b. Show that {e^ax, e^bx} is a linearly independent subset of the vector space C[0, 1].

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