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In the vector space C[0.1], prove that the vectors (i.e., functions) sin x and cos x...

In the vector space C[0.1], prove that the vectors (i.e., functions) sin x and cos x are linearly independent.

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Claime! Sinx and Cosx are linearly Independent. We will prove by contradiction. Let Sinx and Cost are dependent. - CSn = 4C GC, sin ten Op Cost = 0 c. I + C2 = 0 C + C₂ Jz = 0 - 1 Gising + C₂ Cos I = 0 C, +at-o a cite=0 – Will from Eq (o & i & lligar

please ratingIn Worshion theosam, Two fonction Son) are independent, ist and warskion=det fra) 2xs7 ne gla) V NEC Vector Space

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