Subspaces in R4: Get Started & Understand Now - Physics Forums
Mar 7, 2006 · W is defined as the set of vectors in R4 satisfying the equation x1 + x3 = x2 + x4, and it qualifies as a subspace of R4. To verify this, one must check the three main properties: …
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · I have a question that states: Let a, b, and c be scalers such that abc is not equal to 0. Prove that the plane ax + by + cz = 0 is a subspace of R^3.
Determining if a set is a subspace. • Physics Forums
Oct 5, 2014 · I am trying to determine how to tell if a set is a subspace. The problem reads like this: Determine if the described set is a subspace. If so, give a proof. If not, explain why not. …
Determine whether or not something is a subspace
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 …
Why Does a Subset of a Vector Space Need the Zero Vector to Be …
Feb 7, 2008 · If each subspace has its own zero vector, then combine these subspaces in order to get a bigger subspace or even the whole space. We will get bunch of different zeros and the …
Geometric Description of Subspace Spanned by Set S
Nov 5, 2014 · Homework Statement Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span...
What is the Role of Subspace in Sci-Fi Universes?
Dec 19, 2004 · Subspace is a term frequently used in science fiction, particularly in shows like Star Trek and Stargate, to describe a hypothetical dimension that allows for faster-than-light …
Proving Subspace of Mnn: AB=BA for Fixed nxn Matrix B
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...
Show that a line in R2 is a subspace - Physics Forums
Mar 11, 2014 · Homework Statement Show that a line in R2 is a subspace if and only if it passes through the origin (0,0) The Attempt at a Solution Let A set of vectors be the subset of the …
Is a subspace still valid without the zero vector? - Physics Forums
Jan 21, 2009 · No, because the subspace will have negatives of elements, i.e., for all v an element of V, (-1)v or -v will be an element. For the subspace to be closed under addition (a …