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 May 6th, 2019, 09:05 PM #1 Member   Joined: Apr 2017 From: India Posts: 73 Thanks: 0 Quotient space If W is a subspace of a vector space V over the field (Z3) Integer modulo 3 such that Dim(V)=7 and Dim(W)=4, then the number of element in V/W is how much? I can only deduce that number of elements in the basis of V/W will be 3. How to find the total number of elements in V/W? May 7th, 2019, 04:22 PM   #2
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 Originally Posted by shashank dwivedi If W is a subspace of a vector space V over the field (Z3) Integer modulo 3 such that Dim(V)=7 and Dim(W)=4, then the number of element in V/W is how much? I can only deduce that number of elements in the basis of V/W will be 3. How to find the total number of elements in V/W?
Wouldn't it be 27? $|\mathbb Z_3| = 3$ and if $V$ has dim 7, $|V| = 3^7$. Likewise $|W| = 3^4$ and $|V/W| = 27$. That's because each coset of $W$ has the same number of elements, namely $3^4$, so that there must be $3^3 = 27$ distinct cosets. Tags quotient, space Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post BenFRayfield Number Theory 0 October 15th, 2016 11:46 AM allyvene Linear Algebra 0 October 1st, 2014 05:46 PM OriaG Linear Algebra 0 October 17th, 2013 05:34 AM lorereds Topology 0 September 7th, 2011 06:13 AM genoatopologist Real Analysis 2 January 17th, 2009 05:38 AM

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