Linear Combinations and Spans

Saturday, 11 August 2018

12:58 PM

A span is NOT a linear combination

 

Linear Combination - constrained within a vector space

 

Spanning Set
=V

 

 

Prove that 1, x, x2 is a spanning set for

For any polynomial p(x) in , we can write





 





Equate the coefficients







 

…

The system is consistent, there exists

 

For one positive linear combination, we choose a value for the non-leading variable -





 

Hence,

 

 

 Revise how to check for solutions of a matrix, one solution, no solutions, infinite solutions