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.
Linear Algebra: Prove that the set of invertible matrices is a Subspace
Jan 27, 2013 · Homework Statement Is U = {A| A \\in nℝn, A is invertible} a subspace of nℝn, the space of all nxn matrices? The Attempt at a Solution This is easy to prove if you assume the …
Dimension of a vector space and its subspaces • Physics Forums
Jan 24, 2024 · Can a vector subspace have the same dimension as the space it is part of? If so, can such a subspace have a Cartesian equation? if so, can you give an example. Thanks in …
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. …
Upper trianglar matrix is a subspace of mxn matrices
Oct 9, 2016 · Homework Statement Prove that the upper triangular matrices form a subspace of ##\\mathbb{M}_{m \\times n}## over a field ##\\mathbb{F}## Homework EquationsThe Attempt …
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...
Is there a symbol for indicating one vector space is a subspace of ...
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...
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 …
Show that a "cross" is not a topological manifold - Physics Forums
Jul 30, 2024 · Hi, I've a doubt about the following example in "Introduction to Manifold" by L. Tu. My understanding is that if one assumes the subspace topology from ##\\mathbb R^2## for …