Question: Please help me by solve this problem. Thanks in advance. 1. Consider the following subset S C R5 T2 S = : 1 + 3.r2

Please help me by solve this problem. Thanks in advance.

1. Consider the following subset S C R5 T2 S = : 1 + 3.r2 - 213 = 0, $1, 12, 13, DA, I, ER (a) Show that S is a subspace of R5. (b) Find a basis and dimension of S. (c) "Let V be a vector space with dim(V) = n. Then any subset of n vectors is a basis of V." Do you agree or disagree? Explain briefly. Provide an example in favor of your argument

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