Linear Independence of Vectors: Why Determinant ≠ 0?
Apr 29, 2013 · If you put your vectors in a matrix, you get a linear function identified by the matrix. If you can "reach" all of $\mathbb R^3$ with this function, your vectors are linearly independent.
Characterizing linear independence in terms of span
Mar 2, 2025 · Undergrad Characterizing linear independence in terms of span psie Mar 2, 2025 Linear algebra Linear independence
Checking the linear independence of elements of 2 X 2 matrices
Aug 13, 2018 · Checking the linear independence of elements of 2 X 2 matrices Pushoam Aug 13, 2018 Elements Exercise Independence Linear Linear independence Matrices Vector space Click For …
Characterizing Affine Independence • Physics Forums
Nov 9, 2011 · Basically, affine independence is a version of linear independence that doesn't depend on basepoints. You have n+1 points. Take one of them as a reference point. That gives you n vectors. …
Linearly independent but not orthogonal, how come? - Physics Forums
Jul 16, 2008 · Hi everyone, I was reading about Gram-Schmidt process of converting two linearly independent vectors into orthogonal basis. But, as I understand, if two...
Linear independence of orthogonal and orthonormal sets?
Apr 20, 2010 · (Note: this isn't a homework question, I'm reviewing and I think the textbook is wrong.) I'm working through the Gram-Schmidt process in my textbook, and at the end of every chapter it starts …
Confused about small detail in rank-nullity theorem
Mar 7, 2025 · TL;DR I'm reading about the rank-nullity theorem in Linear Algebra by Friedberg et al. At the end of the proof, they claim that the vectors that span the range of the linear transformation and …
Conflicting definitions of linear independence - Physics Forums
Jul 25, 2025 · Linear Algebra - Linear (in)dependence of a set May 27, 2017 Replies 2 Views 2K Isomorphisms preserve linear independence Mar 14, 2019 Replies 2 Views 2K Determining value of …
Linear Independence: V1-V4 in R4 - True or False? - Physics Forums
Sep 16, 2009 · Homework Statement If V1...V4 are linearly independent vectors in R4, then {V1, V2, V3} are also linearly independent. True or False. The Attempt at a Solution My solution involved reducing …
Proving Linear Independence of u, v and w • Physics Forums
Sep 26, 2010 · Homework Statement "if u,v,w are linearly independent then au+bv+cw=0 for some a,b,c in R" first of all is this correct? and how do i proof if...