Finding Vectors to Span Set W: Can u and v Fully Represent W?

Thread starter cdub2
Start date Nov 6, 2009
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Set Span Vectors

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To determine if vectors u and v can fully represent the set W, defined by the vector form (-5b-4c, b, c), the discussion focuses on finding appropriate vectors that span W. The hint provided suggests expressing the components of W in terms of b and c, leading to the equations x = -5b - 4c, y = b, and z = c. Participants are encouraged to explore linear combinations of potential vectors u and v that can generate all vectors in W. The goal is to identify specific vectors that satisfy the spanning condition for the set W. Understanding the relationships between b and c is crucial for solving this problem effectively.

Nov 6, 2009

cdub2

I am having some trouble with this problem...

Let W be the set of all vectors of the form:

(-5b-4c
b
c)

^ (that is supposed to be in vector form)

Find vectors u and v such that W = Span {u,v}.

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Nov 6, 2009

Mark44

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Hint:
x=-5b-4c
y=1b+0c
z=0b+1c

Nov 6, 2009

cdub2

thanks !

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