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Let V=$R^3$ & W be a subspace of V generated by (1,0,0) , (1,1,0). Find basis for quotient space $V/W$.

For finite dimensional vector spaces we have that $$ \dim V = \dim Im F + \dim \ker F, $$

So according to this we must have dimension for $V/W$ as 1.

Now I extend basis for W to basis for V then

Clearly I should have basis for $V/W$ =(0,0,1).

Am I right here?

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    $(0,0,1) \not\in V/W$. I think you mean $\{(0,0,1) + W\}$ which is indeed a basis. – 2017-02-26
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    Yes you are right . Thanks for correction. – 2017-02-26
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    No problem. :-) – 2017-02-26

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