For each of the following, show that the given vectors are linearly independent in C[0, 1]. (a)

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For each of the following, show that the given vectors are linearly independent in C[0, 1].
(a) cos πx, sin πx
(b) x3/2, x5/2
(c) 1, ex + e-x, ex - e-x
(d) ex, e-x, e2x
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