SOLUTION: Let {a1,...,ap} be a set of vectors from R^n. If a1=x2a2+...+xpap where x2...xp are scalars, then span(a1...ap) = span(a2...ap). I need assistance showing that this statement is
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-> SOLUTION: Let {a1,...,ap} be a set of vectors from R^n. If a1=x2a2+...+xpap where x2...xp are scalars, then span(a1...ap) = span(a2...ap). I need assistance showing that this statement is
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Question 107124: Let {a1,...,ap} be a set of vectors from R^n. If a1=x2a2+...+xpap where x2...xp are scalars, then span(a1...ap) = span(a2...ap). I need assistance showing that this statement is true. Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Remember the span of a set of vectors is the set of all linear combinations of every vector in the set. In other words...
for some scalar
But since , we can replace with the expanded notation and simplify.
The final result will be
So here is one way you could go about solving this proof:
(