Aug 25, 2006 · R^2 is isomorphic to the subset (a,b,0) of R^3, but it's also isomorphic to infinitely many other subspaces of R^3 (any 2 dimensional one). As such, there's no canonical …

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 …

Mar 15, 2011 · Prove your answer. b) Determine whether or not A ∪ B is a vector subspace of V . Prove your answer. My strategy for this is to find two subspaces in V and find a counter claim …

Oct 31, 2012 · I am trying to visualize the subsppace topology that is generated when you take the Rationals as a subset of the Reals. So if we have ℝ with the standard topology, open sets …

Jun 10, 2011 · Here's an example, "If L is a closed linear subspace of H, then the set of of all vectors in H that are orthogonal to every vector in L is itself a closed linear subspace". But …

Sep 6, 2009 · Homework Equations is a subspace of if is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication. The definition …

Nov 3, 2013 · Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311.1.5.8 Ax=b in parametric vector form,

Nov 27, 2020 · A few things; the subspace is also a space of functions, and the requirement of a zero vector in this context means that the subspace must contain a zero function , i.e. . Since , …

Oct 27, 2008 · a)is S closed under addition? b) is S closed under scalar multiplication? Homework Equations S is a subspace of V if it is closed under addition and scalar multiplication. The …

Jan 23, 2016 · The smallest subspace containing vectors in the list is . How can one know how small a subspace is? initially I thought it was determined from the number of elements in the …