Exam 5¶
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 5.
Question 1¶
Find area of transformed triangle.
- (1 pt) Find area of given triangle (geometrically or using det)
(-1 pt) Area is incorrect or missing work [IA]
- (3 pts) Find area of transformed triangle (several good methods)
(-1 pt) Minor arithmetic error [MinE]
(-2 pts) Major mathematical error [MajE]
(-3 pts) Method is not sound or work is missing [NS]
Question 2¶
Given e-val, find basis of e-space.
- (1 pt) Plug into \(A-\lambda I\)
(-1 pt) Matrix is missing or incorrect [IM]
- (2 pts) Find solutions
(-1 pt) Minor error in computation [MinE]
(-2 pts) Major error in computation [MajE]
- (1 pt) Identify basis
(-1 pt) Basis is missing or incorrect [MB]
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¶
Find general solution.
- (3 pts) Calculate e-vals and e-vecs.
- (2 pts) Eigenvalues
(-1 pt) Minor error in computation [MinE]
(-2 pts) Major error in computation [MajE]
- (1 pt) Eigenvectors
(-1 pt) E-vecs are missing or incorrect [IV]
- (1 pt) Put into general solution formula.
(-1 pt) Multiple or major errors in formula [IA]