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. x264 [Tamil +. Movie Dialogues, Happy New Year 2014, Cobbler, Hd 1080p,.. bodhidharma full movie in tamil hd 1080p Â· Hindi Hd 1080pÂ . 7:30. 2013 Full Movie HD 1080p Tamil[rec].Q:
How to explain that $\dim(V) = 1$
I’ve asked a question with the title of this topic but I don’t think it’s clear. I’m sorry if this topic is already answered.
The question is: Let $W$ be a subspace of $V$. Assume that $\dim(W)
eq 1$. And let $v$ be an element of $W$ of minimal norm $\|v\|$. Prove that there exists $w \in W$ such that $\|w\| = \|v\|$.
So far I’ve done this:
I’ve proved that $V/W$ is a vector space.
I’ve proved that $\dim(V/W) = \dim(V) – \dim(W)$
I’ve proved that the norm of a vector is invariant by right multiplication by a constant (this is where I’m stuck).
What I’m going to ask is: Can somebody explain to me in a detailed way the ideas I’ve used to solve this question? I think that’s the best way to learn.
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