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Linear Combinations and Spans

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1) Determine if b is a linear combination of , .

2) List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch.

a)

b)

3) Let For what value(s) of h is b in the plane spanned by and ?

4) True or false, explain answer.

a) Any list of five real numbers is a vector in .
b) The vector u results when a vector u-v is added to the vector v.
c) The weights in a linear combination cannot all be zero.
d) When u and v are nonzero vectors, Span {u,v} contains the line through u and the origin.
e) Asking whether the linear system corresponding to an augmented matrix
[ b] has a solution amounts to asking whether b is in Span { }.

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Linear combinations and spans are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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