Solution Found!
Spanning Sets In Exercises 1924, determine whether the set
Chapter 4, Problem 4.4.20(choose chapter or problem)
Spanning Sets In Exercise, determine whether the set S spans \(R^{3}\). If the set does not span \(R^{3}\), then give a geometric description of the subspace that it does span.
\(S=\{(5,6,5),(2,1,-5),(0,-4,1)\}\)
Questions & Answers
QUESTION:
Spanning Sets In Exercise, determine whether the set S spans \(R^{3}\). If the set does not span \(R^{3}\), then give a geometric description of the subspace that it does span.
\(S=\{(5,6,5),(2,1,-5),(0,-4,1)\}\)
ANSWER:Step 1 of 3
Consider the definition of the span of a set,if \(S=v_{1}, v_{2}, \ldots \ldots v_{k}\) is a set of vectors in a vector space V,then the span of S is the set of all linear combinations of the vectors in S.
\(\operatorname{span}(S)=c_{1} v_{1}+c_{2} v_{2}+\ldots .+c_{k} v_{k}: c_{1}, c_{2}, \ldots c_{k}\) are real numbers.
The span S is denoted by
span(S) or span \(v_{1}, v_{2}, \ldots, v_{k}\) or that S spans V.