Jan 24, 2024 · My thought was that was a vector space and a subspace with an uncountably infinite index. I then confused index and dimension instead of building a correct counterexample.

Mar 7, 2006 · I'm so lost! 1. W is the set of all vectors in R4 such that x1 + x3 = x2 + x4. Is W a subspace of R4 and Why? How do i get started here? I'm thoroughly confused on this whole idea of …

Mar 4, 2008 · So I'm considering dimensions of real vector spaces. I found myself thinking about the following: So for the vector space R2 there are the following possible subspaces: 1. {0} 2. R2 3. All …

Sep 18, 2012 · The discussion focuses on determining which sets of polynomials in P4 qualify as subspaces. It is established that only the set of polynomials p (x) where p (0) = 0 is a subspace, as it …

Apr 27, 2011 · Hi all, I was just wondering, is there is a particular symbol to say V is a subspace of W? I suppose V\subsetW works if I describe each (sub)space in...

Sep 15, 2011 · Homework Statement Prove that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B, is a subspace of Mnn. Homework Equations u + v is in the same vector space …

Feb 5, 2007 · For a vector x in R^4, the dimension of the subspace S spanned by its permutations can take on values of 0, 1, 3, or 4. A zero-dimensional case occurs when x is the zero vector. A one …

Feb 28, 2008 · Every non-empty subset W of a vector space V over the field F2 is a subspace if it is closed under addition. To confirm W is a subspace, it must also be closed under scalar multiplication, …

Mar 7, 2009 · My understanding of the subspace still isn't solid enough, so I want to know what I know so far is at least correct. By definition, a set of vectors S of Rn is called a subspace of Rn iff for all …

Oct 13, 2008 · If W is a vector space itself, with the same vector space operations as V has, then it is a subspace of V. To use this definition, we don't have to prove that all the properties of a vector space …