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Thread: Prove that V is a subspace of Rn

  1. #1
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    Prove that V is a subspace of Rn

    Let V = {x E Rn | 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 Rn. Prove that V is a subspace of Rn.


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  2. #2
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    Re: Prove that V is a subspace of Rn

    you need to show that

    $\forall x,y \in V,~a,b \in \mathbb{R},~a x + b y \in V$
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  3. #3
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    Re: Prove that V is a subspace of Rn

    Following on what romsek said, since A is a linear transformation, what is A(ax+ by)?
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