Exercises 5.30 Timed Chapter Exam
True.
- The vector space of all polynomials with finite degree has a basis, \(B = \{1,x,x^2,x^3,\dots\}\text{,}\) which is infinte.
False.
- The vector space of all polynomials with finite degree has a basis, \(B = \{1,x,x^2,x^3,\dots\}\text{,}\) which is infinte.
This is an
<exercises> division, as a peer of the <section> in this <chapter> of a <book>. It is also setup as a Runestone timed exam. So it is an example of how you might have a per-chapter exam. This contrasts with an earlier timed exam which is constructed as a per-section exam (Exercises 5.21). The exercises are the same here, but in a different order. As a test, this exam is “pauseable” and has a 15 minute time limit.
2. True/False.
Every vector space has finite dimension.
Hint.
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 3.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
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