MA 125 Exam 2 Practice Material

MA 125 Exam 2
Arosh De Silva

TOTAL POINTS


ÊÊ + 1 pts Part (b): Gaussian elim. used to solve,
QUESTION 1
but with mistake
1 Q1
ÊÊ + 0 pts Part (b): Blank or totally incorrect
✓ + 10 pts Everything correct and work shown
ÊÊ + 3 pts Part (c): Correct (relative to Part (a)) and
ÊÊ + 0 pts Everything incorrect or blank
work shown
ÊÊ + 5 pts Part (a): Correct and work shown
ÊÊ + 2.5 pts Part (c): $$\left[\begin{array}{cc} 2 &
ÊÊ + 4 pts Part (a): A correct approach, but
2\\-2 & 1\end{array}\right]A^{-1}$$ multiplied
arithmetic mistake
with mistake or left factored
ÊÊ + 3 pts Part (a): Partially correct approach, for
ÊÊ + 2 pts Part (c): $$A^{-1}\left[\begin{array}{cc} 2
example mistake in inverse formula or
& 2\\-2 & 1\end{array}\right]$$ computed
augmented matrix set up with wrong matrices.
ÊÊ + 1.5 pts Part (c): A product of
ÊÊ + 2 pts Part (a): Partially correct approach, for
$$\left[\begin{array}{cc} 2 & 2\\-2 &
example mistake in inverse formula or
1\end{array}\right]$$ with $$A$$ computed
augmented matrix set up with wrong matrices.
ÊÊ + 1 pts Part (c): $$\left[\begin{array}{cc} 2 & 2\\-
Arithmetic mistake as well
2 & 1\end{array}\right]$$ used in some way other
ÊÊ + 1.5 pts Part (a): Determinant computed
than product with $$A^{-1}$$ or $$A$$
correctly, no other progress
ÊÊ + 0.5 pts Part (c): Arithmetic mistake or answer
ÊÊ + 1 pts Part (a): Determinant computed but with
left factored
mistake, no other progress
ÊÊ + 0 pts Part (c): Blank or totally incorrect
ÊÊ + 0 pts Part (a): Blank or totally incorrect
ÊÊ + 0 pts CORRECT ANSWER WITH NO JUSTIFYING
ÊÊ + 2 pts Part (b): Correct (relative to Part (a)) and
WORK, OR OTHERWISE SUSPICIOUS
work shown (including if solution is found by
Gaussian elim. or other method). QUESTION 2
ÊÊ + 1.5 pts Part (b): Correct except for arithmetic
2 Q2
mistake or typo
✓ + 10 pts Everything correct, with work shown
ÊÊ + 1 pts Part (b): $$A^{-1}\left[\begin{array}{c}
ÊÊ + 9.5 pts Everything is correct, except row
a\\ b\end{array}\right]$$ computed with mistake
echelon form is not Kuttler version (ie. some
in multiplication formula, or the final answer is
leading entries not 1).
given with incorrect use of notation

, ÊÊ + 9.5 pts Everything correct, except arithmetic some operations which are not actually
mistake in finding solutions in part (c) elementary row operations (beyond arithmetic
ÊÊ + 9 pts Everything is correct except Part (b) has mistake).
an arithmetic mistake ÊÊ + 0 pts Part (b): totally incorrect or blank

ÊÊ + 7 pts Part (a) and (b) both correct with work ÊÊ + 3 pts Part (c): Correct given part (b)
shown ÊÊ + 2 pts Part (c): arithmetic mistake finding

ÊÊ + 1 pts Part (a): correct solutions
ÊÊ + 0.5 pts Part (a): typo(s) (e.g. (0 2 2) instead of ÊÊ + 1.5 pts Part (c): infinite solution set but
(2 2 0) in second row, otherwise correct incorrect from setup
ÊÊ + 0.5 pts Part (a): matrix equation $$Ax=b$$ ÊÊ + 1.5 pts Part (c): Answer given in form of
given instead of augmented matrix reduced system of two equations, but solution set
ÊÊ + 0.5 pts Part (a): correct (or with typos) is not parameterized.
coefficient matrix only ÊÊ + 1 pts Part (c): Some relevant calculations, but
ÊÊ + 0.5 pts Part (a): missing row, otherwise correct conceptual mistake in computing solution(s), such
ÊÊ + 0 pts Part (a): totally incorrect or blank as ignoring a row or taking incorrect conclusion
ÊÊ + 6 pts Part (b): correct relative to part (a) with from matrix.
work shown ÊÊ + 1 pts Part (c): Solutions not found, but
ÊÊ + 5.5 pts Part (b): correct, except row echelon statement that there are infinitely many solutions,
form is not Kuttler version (ie. some leading with some correct reasoning
entries not 1). ÊÊ + 0.5 pts Part (c): Solutions not found, but
ÊÊ + 5 pts Part (b): arithmetic mistake(s) in row statement that there are infinitely many solutions,

reduction, reaching a matrix in row echelon form with incorrect/no reasoning
ÊÊ + 4.5 pts Part (b): correct, except arithmetic ÊÊ + 0 pts Part (c): totally incorrect or blank
mistake and row echelon form is not Kuttler ÊÊ + 7 pts Maximum points for parts (a)-(c) correct
version (ie. some leading entries not 1). but with simplified system (e.g. removing an
ÊÊ + 4 pts Part (b): Every row operation is correct equation). If above items applied total less than 7,
or only arithmetic mistake but last step is not in use those.

the correct echelon form. ÊÊ + 0 pts Completely incorrect
ÊÊ + 3 pts Part (b): correct row operations to row ÊÊ + 0 pts CORRECT ANSWER WITH NO JUSTIFYING

echelon form on coefficient matrix (or with WORK, OR OTHERWISE SUSPICIOUS
arithmetic mistakes), but same operations
QUESTION 3
incorrectly applied to solution vector
3 Q3
ÊÊ + 1 pts Part (b): Result is in row echelon form
✓ + 10 pts Everything correct and work shown
(Kuttler version or otherwise), but obtained by