<solutions divisional="hint answer solution">
<title>Hints and Answers to Selected Exercises</title>
</solutions>
Appendix D Hints and Answers to Selected Exercises
View Source for solutions
II Algebra
3 Runestone Testing
3.8 True/False Exercises
3.8.1. True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws" />. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
3.9 Multiple Choice Exercises
3.9.1. Multiple-Choice, Not Randomized, One Answer.
Hint 1.
View Source for hint
<hint>
<p>
What did you see last time you went driving?
</p>
</hint>
What did you see last time you went driving?
Hint 2.
View Source for hint
<hint>
<p>
Maybe go out for a drive?
</p>
</hint>
Maybe go out for a drive?
3.9.2. Multiple-Choice, Not Randomized, Multiple Answers.
Hint.
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<hint>
<p>
Do you know the acronym<ellipsis /><acro>ROY G BIV</acro> for the colors of a rainbow,
and their order?
</p>
</hint>
Do you know the acronym…ROY G BIV for the colors of a rainbow, and their order?
3.9.3. Multiple-Choice, Randomized, One Answer.
Hint 1.
View Source for hint
<hint>
<p>
What did you see last time you went driving?
</p>
</hint>
What did you see last time you went driving?
Hint 2.
View Source for hint
<hint>
<p>
Maybe go out for a drive?
</p>
</hint>
Maybe go out for a drive?
3.9.4. Multiple-Choice, Randomized, Multiple Answers.
Hint.
View Source for hint
<hint>
<p>
Do you know the acronym<ellipsis /><acro>ROY G BIV</acro> for the colors of a rainbow,
and their order?
</p>
</hint>
Do you know the acronym…ROY G BIV for the colors of a rainbow, and their order?
3.9.5. Mathematical Multiple-Choice, Not Randomized, Multiple Answers.
Hint.
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<hint>
<p>
You can take a derivative on any one of the choices to see if it is correct or not,
rather than using techniques of integration to find
<em>a single</em> correct answer.
</p>
</hint>
You can take a derivative on any one of the choices to see if it is correct or not, rather than using techniques of integration to find a single correct answer.
3.10 Parsons Exercises
3.10.1. Parsons Problem, Mathematical Proof.
Hint.
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<hint>
<p>
Dorothy will not be much help with this proof.
</p>
</hint>
Dorothy will not be much help with this proof.
3.10.6. Parsons Problem, Mathematical Proof, Numbered Blocks.
Hint.
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<hint>
<p>
Dorothy will not be much help with this proof.
</p>
</hint>
Dorothy will not be much help with this proof.
3.12 Matching Exercises
3.12.3. Matching Problem, Linear Algebra.
Hint.
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<hint>
<p>
For openers, a basis for a subspace must be a
<em>subset</em> of the subspace.
</p>
</hint>
For openers, a basis for a subspace must be a subset of the subspace.
3.13 Clickable Area Exercises
3.13.3. Clickable Areas, Text in a Table.
Hint.
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<hint>
<p>
Python boolean variables begin with capital latters.
</p>
</hint>
Python boolean variables begin with capital latters.
3.18 Fill-In Exercises
3.18.10. Fill-In, Dynamic Math with Simple Numerical Answer.
3.18.11. Fill-In, Dynamic Math with Formulas as Answers.
3.18.12. Fill-In, Dynamic Math with Interdependent Formula Checking.
3.19 Hodgepodge
3.19.1. With Tasks in an Exercises Division.
3.19.1.a True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws" />. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
3.20 Exercises that are Timed
Timed Exercises
3.20.1. True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws" />. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
3.20.2. Multiple-Choice, Not Randomized, One Answer.
Hint 1.
View Source for hint
<hint>
<p>
What did you see last time you went driving?
</p>
</hint>
What did you see last time you went driving?
Hint 2.
View Source for hint
<hint>
<p>
Maybe go out for a drive?
</p>
</hint>
Maybe go out for a drive?
3.27 Group Exercises
3.27.1. Multiple-Choice, Not Randomized, One Answer.
Hint 1.
View Source for hint
<hint>
<p>
What did you see last time you went driving?
</p>
</hint>
What did you see last time you went driving?
Hint 2.
View Source for hint
<hint>
<p>
Maybe go out for a drive?
</p>
</hint>
Maybe go out for a drive?
