a) Prove that a super set of a linearly dependent set in a vector spa…

Question

a) Prove that a super set of a linearly dependent set in a vector space in linearly dependent.

b) Verify Rank-Nullity theorem for the linear transformation $T : R^2 \to R^2$ defined as $T(x,y) = (x+y, x-y)$ for any $x, y \in R$.

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