Consider the following subset SC R X2 S = : x1 + 3x2 – 2x3 = 0, x1, x2, X3, X4, X5 E R 13 - X4 X5 (a) Show that S is a subspace of R°. (b) Find a basis and dimension of S. (c) “Let V be a vector space...

Extracted text: Consider the following subset SC R X2 S = : x1 + 3x2 – 2x3 = 0, x1, x2, X3, X4, X5 E R 13 - X4 X5 (a) Show that S is a subspace of R°. (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.