Exam 2¶
Each question will be graded out of 4 points, with partial credit given for incomplete or incorrect answers. To pass the exam, you will need at least 10 points total, which is an average of 2.5 for each question.
Next to each part of the rubrics, you will see error codes in square brackets. These error codes are will be used to indicate why any points were taken off on your exam papers.
Below are the rubrics for exam 2.
Question 1¶
Is the subset a subspace?
- (1 pt) Correct answer
(-1 pt) Missing or incorrect answer [IA]
- (3 pts) Explain answer
- Answer YES
- Provide reasoning (3 points possible)
(-0 pt) Prove that both axioms hold
(-1 pt) Prove only one of the axioms [MA]
(-2 pts) Attempt to show both axioms [IR]
(-3 pts) Reasoning is not sound [NS]
- Provide an example (1 point possible)
(-0 pts) Demonstrate both closure axioms [EX]
(-1 pt) Example does not demonstrate both axioms [ND]
- Answer NO
- Provide reasoning (3 points possible)
(-0 pts) Reasoning explains why axioms are violated
(-2 pts) Reasoning is sound but not a proof [SR]
(-3 pts) Reasoning is not sound [NS]
- Provide an example (3 points possible)
(-0 pts) Example shows that one of the closure axioms is violated
(-3 pts) Example does not show one of the axioms is violated [NX]
Question 2¶
Find a basis.
- (1 pt) All work included (including calculator steps)
(-1 pt) Most of the work is not included [MW]
- (1 pt) Correct echelon form
(-1 pt) Echelon form is incorrect [IE]
- (2 pts) Correct answer based on echelon form
(-2 pts) No work after echelon form [MA]
(-2 pts) Answer is missing or has major error [IA]
(-1 pt) Answer has a minor error [ME]
Question 3¶
True or False?
- (1 pt) Correct answer
(-1 pt) Answer is either incorrect or missing [IA]
- (3 pts) Explain answer
- Answer TRUE
- Provided reasoning (3 points possible)
(-1 pt) Reasoning is sound but not a proof [RS]
(-2 pts) Some of the reasoning is sound [PS]
(-3 pts) Reasoning is not sound [NS]
- Provided an example (2 points possible)
(-0 pts) Example supports an answer of TRUE [EX]
(-1 pt) Example supports an answer of FALSE (is a counterexample) [CX]
(-2 pts) Example is incorrect or not relevant [NX]
- Answer FALSE
- Provided reasoning (3 points possible)
(-1 pt) Reasoning is sound but not a proof of the negative [RS]
(-2 pts) Some of the reasoning is sound [PS]
(-3 pts) Reasoning is not sound [NS]
- Provided an example (3 points possible)
(-0 pts) Counterexample [CX]
(-2 pts) Example supports an answer of TRUE [EX]
(-3 pts) Example is incorrect or not relevant [NX]
Question 4¶
Is the set a basis of \(\mathbb{R}^3\)?
- (1 pt) Correct echelon form
(-1 pt) Echelon form is incorrect [IE]
- (3 pts) Correct answer based on echelon form
(-1 pt) Answer is missing [MA]
(-1 pt) Answer is incorrect [IA]
(-2 pt) Explanation is missing or has a major error [EE]
(-1 pt) Explanation has a minor error [ME]