Finding non-trivial linear combination • Physics Forums
Mar 23, 2011 · The discussion revolves around demonstrating the linear dependence of a set of vectors by finding a nontrivial linear combination that results in the zero vector. Participants are tasked with …
Determine if vector b is a linear combination of vectors a1, a2, a3.
Feb 18, 2013 · One participant describes their method of forming a coefficient matrix with vectors a1, a2, a3 and vector b, and notes that the row-reduced form produces a consistent system with a free …
Finding the Scalar for a Vector in a Linear Combination
Apr 8, 2005 · The discussion revolves around expressing a vector b as a linear combination of given vectors v1, v2, and v3, and subsequently determining if v1 can be expressed as a linear combination …
Difference between a spanning and linear combination?
Aug 15, 2010 · The discussion revolves around the concepts of span and linear combinations in the context of vector spaces. Participants explore the definitions, relationships, and conditions under …
Dumb question about this linear algebra equation - Physics Forums
Jul 21, 2012 · The discussion revolves around demonstrating that any vector V in a plane can be expressed as a linear combination of two non-parallel vectors A and B. The original poster attempts …
Finding Unique Vector Representation • Physics Forums
Feb 1, 2007 · The discussion centers on finding a unique vector representation in the vector space F^4 using the basis { (1,1,1,1), (0,1,1,1), (0,0,1,1), (0,0,0,1)}. The participants clarify that to express an …
Are These Vectors Linearly Independent? • Physics Forums
Sep 10, 2012 · Exploratory, Assumption checking, Problem interpretation Participants express uncertainty about how to start the problem and discuss the setup of a linear combination involving …
Does a Linear Combination of Vectors in an Infinite Set Have to Be ...
Sep 30, 2013 · The discussion revolves around the nature of linear combinations of vectors in the context of infinite sets spanning a vector space. Participants explore whether such combinations …
Difference Between Lines and Vectors (Linear Combination Problem)
Feb 10, 2014 · Another participant explains the relationship between vectors and points in space, emphasizing the importance of coordinate systems in understanding vector representation. …
How to Prove that the Span of k-1 Vectors is also the Span of V?
Apr 28, 2012 · This discussion focuses on proving that if a vector space V is spanned by k vectors {v1, v2, ..., vk} and one vector can be expressed as a linear combination of the others, then the span of …