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Reading Questions 20.4 Reading Questions

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1.

Why do the axioms of a vector space appear to only have four conditions, rather than the ten you may have seen the first time you saw an axiomatic definition?

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2.

The set V=Q(11)={a+b11∣a,b∈Q} is a vector space. Carefully define the operations on this set that will make this possible. Describe the subspace spanned by S={u}, where u=3+2711∈V.

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3.

Write a long paragraph, or a short essay, on the importance of linear independence in linear algebra.

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4.

Write a long paragraph, or a short essay, on the importance of spanning sets in linear algebra.

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5.

“Linear algebra is all about linear combinations.” Explain why you might say this.