Some problems – linear independent

BT về độc lập tt.

Prob 1. Prove that any three vectors in \mathbb{R}^2 are linearly dependent. Generalize this result to \mathbb{R}^n.

Prob 2. Show that the function x, e^x sinx, e^x cosx form a linearly independent subset of the vector space C[0,\pi].

Trích: Derek Robinson, A course in linear algebra with applications, World Scientific 2006.

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