Let V = {x E R^{n} | Ax= λx} where A is an n x n matrix and λ is a real scalar, together with the usual operations for vector addition and scalar multiplication from R^{n}. Prove that V is a subspace of R^{n}.
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you need to show that $\forall x,y \in V,~a,b \in \mathbb{R},~a x + b y \in V$
Following on what romsek said, since A is a linear transformation, what is A(ax+ by)?
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