## Reading Questions 20.4 Reading Questions

###### 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?

###### 2.

The set \(V={\mathbb Q}(\sqrt{11})=\{a+b\sqrt{11}\mid a,b\in{\mathbb Q}\}\) is a vector space. Carefully define the operations on this set that will make this possible. Describe the subspace spanned by \(S=\{\mathbf{u}\}\text{,}\) where \(\mathbf{u}=3+\frac{2}{7}\sqrt{11}\in V\text{.}\)

###### 3.

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

###### 4.

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

###### 5.

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