Exam 3

Sample exam 3

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 3.

Question 1

Is the function a linear transformation?

(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 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 axioms is violated

(-3 pts) Example does not show one of the axioms is violated [NX]

Question 2

Find the matrix representation.

(2 pts) What happens to basis vectors

(-1 pt) One of the basis vectors is missing or incorrect [IB]

(-2 pt) Both of the basis vectors are missing or incorrect [IB2]

(2 pts) Arrange outputs into matrix

(-1 pt) One of the outputs is not arranged into matrix correctly [IM]

(-2 pt) Both of the outputs is not arranged into matrix correctly [IM2]

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 linear transformation invertible?

(1 pt) Find matrix representation.

(-1 pt) Matrix representation is incorrect [MR]

(3 pts) Answer question and explain.
Answer YES

(-0 pts) Pivot in every row and column

(-1 pt) Pivot location does not match answer (e.g. say it is onto because pivot in every column) [PL]

(-2 pts) Answer mentions pivots but is incorrect. [IP]

(-3 pts) Answer does not mention pivots [NP]

Answer NO

(-0 pts) Row or column missing a pivot

(-1 pt) Missing pivot does not match answer (e.g. say it is not 1-1 because row missing pivot) [PL]

(-2 pts) Answer mentions pivots but is incorrect. [IP]

(-2 pts) Answer does not mention pivots [NP]