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Suggestion for LE2 #334 (#460)
* Suggestion for LE2 #334 * Merge in main (#473) * made PS2 notation to be consistent with PS1; addresses PS2 vs PS1 notation for power series #41 (#454) * Update presentations on website (#456) * Format presentations, update citation * Add posters * Update site/pages/about.md Co-authored-by: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> --------- Co-authored-by: jkostiuk <kostiuk.jordan@gmail.com> * Added answers for Calculus LT1 MCQs (#458) * Added Answer for first Calc activity * Answers added to Calculus 1.1 Limits Graphically LT1 * Update ti8 check it (#465) Co-authored-by: Drew Lewis <drew.lewis@gmail.com> Co-authored-by: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> * make second colophon a preface (#464) * Quicker PR previews (#455) * begin refactor: build/deploy are just for full builds * use gitpython to see changed files * get accurate list of changed files * grab changed ptx files * build changed PTX files * add preview action * fix cloudflare requirement * get full history in source checkout * update pretext version * try GitDB fix * specify origin/main * try adding safe directory * try safe directory again * try setting permission in action * try abspath * clean up cruft * try default fetch_depth * restore fetch-depth * use main function * share markdown output * multiline output * check output * write to output file * try backtick interpolation * use single-line markdown * fix quote * smaller test content * try using javascript template * escape ticks * don't escape newline * undo chnages to main * try another xml ID * add base URL to preview message * remove checkit build deletion since we will never send full checkit there * fix string formatting * remove placeholder foo.ptx * Small edit to EL1 (#410) * Precalculus TE1 (#397) Co-authored-by: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> * FN5 addition (#469) * Add more description of TBIL (#467) --------- Co-authored-by: Cory Wilson <40644848+cg2wilson@users.noreply.github.com> Co-authored-by: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> Co-authored-by: jkostiuk <kostiuk.jordan@gmail.com> Co-authored-by: mlamich1 <139090918+mlamich1@users.noreply.github.com> Co-authored-by: TienChih <tien.chih@emory.edu> Co-authored-by: Drew Lewis <drew.lewis@gmail.com> Co-authored-by: Abby Noble <85640990+AbbyANoble@users.noreply.github.com> Co-authored-by: tdegeorge <143553140+tdegeorge@users.noreply.github.com> * added instructor note explaining repetition * moved and expanded instructor's note --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> Co-authored-by: Cory Wilson <40644848+cg2wilson@users.noreply.github.com> Co-authored-by: Drew Lewis <30658947+siwelwerd@users.noreply.github.com> Co-authored-by: mlamich1 <139090918+mlamich1@users.noreply.github.com> Co-authored-by: TienChih <tien.chih@emory.edu> Co-authored-by: Drew Lewis <drew.lewis@gmail.com> Co-authored-by: Abby Noble <85640990+AbbyANoble@users.noreply.github.com> Co-authored-by: tdegeorge <143553140+tdegeorge@users.noreply.github.com>
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‎source/linear-algebra/source/01-LE/02.ptx

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@@ -644,64 +644,96 @@ in many applications we use it for in <xref ref="EV"/>.
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</statement>
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</remark>
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<activity estimated-time='8'>
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<statement>
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<commentary component="instructor">
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<paragraphs>
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<title>Instructor Note</title>
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<p>
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In the following 4-part activity, students make decisions about which row operations are most helpful for them in producing the RREF.
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The matrices appearing in parts (b) and (c) are obtained by applying specific choices of row operations to the matrix appearing previously; the matrix in part (d) is the one that we started with.
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</p>
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<p>
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Consider the matrix
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<me>\left[\begin{array}{cccc}2 &amp; 6 &amp; -1 &amp; 6 \\ 1 &amp; 3 &amp; -1 &amp; 2 \\ -1 &amp; -3 &amp; 2 &amp; 0 \end{array}\right].</me>
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Which row operation is the best choice for the first move in converting to RREF?
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Our experience in facilitating these activities is that student reasoning in part (a) is largely grounded in the production of zeroes, no matter how they appear; because of this, all of the choices in part (a) may appear to be equally valid to them.
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In contrast, choices made in parts (b) and (c) are more constrained as our students recognize the utility of using the marked pivot intentionally to clear entries above and below.
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By revisiting the original matrix in part (d) after marking the pivot position, the instructor can highlight how choices are more intentionally guided by the pivots.
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In turn, this helps students develop a more strategic approach, which is codified in the observation following the activity.
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</p>
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</paragraphs>
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</commentary>
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<activity estimated-time='15'>
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<task>
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<p>
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Consider the matrix:
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<me>\left[\begin{array}{cccc}2 &amp; 6 &amp; -1 &amp; 6 \\ 1 &amp; 3 &amp; -1 &amp; 2 \\ -1 &amp; -3 &amp; 2 &amp; 0 \end{array}\right].</me>
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Which row operation is the best choice for the first move in converting to RREF?
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</p>
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<ol marker="A.">
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<li> Add row 3 to row 2 (<m>R_2+R_3 \rightarrow R_2</m>)
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</li>
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<li> Add row 2 to row 3 (<m>R_3+R_2 \rightarrow R_3</m>)
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</li>
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<li> Swap row 1 to row 2 (<m>R_1 \leftrightarrow R_2</m>)
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</li>
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<li> Add -2 row 2 to row 1 (<m>R_1-2R_2 \rightarrow R_1</m>)
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</li>
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</ol>
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</task>
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<task>
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<p>
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Consider the matrix:
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<me>\left[\begin{array}{cccc} \markedPivot{1} &amp; 3 &amp; -1 &amp; 2 \\ 2 &amp; 6 &amp; -1 &amp; 6 \\ -1 &amp; -3 &amp; 2 &amp; 0 \end{array}\right].</me>
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Which row operation is the best choice for the next move in converting to RREF?
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</p>
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<ol marker="A.">
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<li> Add row 3 to row 2 (<m>R_2+R_3 \rightarrow R_2</m>)
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</li>
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<li> Add row 2 to row 3 (<m>R_3+R_2 \rightarrow R_3</m>)
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</li>
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<li> Swap row 1 to row 2 (<m>R_1 \leftrightarrow R_2</m>)
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</li>
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<li> Add -2 row 2 to row 1 (<m>R_1-2R_2 \rightarrow R_1</m>)
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</li>
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</ol>
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</statement>
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</activity>
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<ol marker="A.">
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<li> Add row 1 to row 3 (<m>R_3+R_1 \rightarrow R_3</m>)
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</li>
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<li> Add -2 row 1 to row 2 (<m>R_2-2R_1 \rightarrow R_2</m>)
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</li>
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<li> Add 2 row 2 to row 3 (<m>R_3+2R_2 \rightarrow R_3</m>)
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</li>
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<li> Add 2 row 3 to row 2 (<m>R_2+2R_3 \rightarrow R_2</m>)
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</li>
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</ol>
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</task>
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<activity estimated-time='7'>
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<statement>
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<task>
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<p>
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Consider the matrix
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<me>\left[\begin{array}{cccc} \markedPivot{1} &amp; 3 &amp; -1 &amp; 2 \\ 2 &amp; 6 &amp; -1 &amp; 6 \\ -1 &amp; -3 &amp; 2 &amp; 0 \end{array}\right].</me>
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Which row operation is the best choice for the next move in converting to RREF?
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Consider the matrix:
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<me>\left[\begin{array}{cccc}\markedPivot{1} &amp; 3 &amp; -1 &amp; 2 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 0 &amp; 1 &amp; 2 \end{array}\right].</me>
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Which row operation is the best choice for the next move in converting to RREF?
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</p>
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<ol marker="A.">
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<li> Add row 1 to row 3 (<m>R_3+R_1 \rightarrow R_3</m>)
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</li>
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<li> Add -2 row 1 to row 2 (<m>R_2-2R_1 \rightarrow R_2</m>)
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</li>
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<li> Add 2 row 2 to row 3 (<m>R_3+2R_2 \rightarrow R_3</m>)
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</li>
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<li> Add 2 row 3 to row 2 (<m>R_2+2R_3 \rightarrow R_2</m>)
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</li>
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</ol>
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</statement>
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</activity>
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<ol marker="A.">
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<li> Add row 1 to row 2 (<m>R_2+R_1 \rightarrow R_2</m>)
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</li>
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<li> Add -1 row 3 to row 2 (<m>R_2-R_3 \rightarrow R_2</m>)
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</li>
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<li> Add -1 row 2 to row 3 (<m>R_3-R_2 \rightarrow R_3</m>)
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</li>
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<li> Add row 2 to row 1 (<m>R_1+R_2 \rightarrow R_1</m>)
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</li>
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</ol>
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</task>
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<activity estimated-time='5'>
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<statement>
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<task>
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<p>
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Consider the matrix
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<me>\left[\begin{array}{cccc}\markedPivot{1} &amp; 3 &amp; -1 &amp; 2 \\ 0 &amp; 0 &amp; 1 &amp; 2 \\ 0 &amp; 0 &amp; 1 &amp; 2 \end{array}\right].</me>
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Which row operation is the best choice for the next move in converting to RREF?
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Consider the matrix:
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<me>\left[\begin{array}{cccc}2 &amp; 6 &amp; -1 &amp; 6 \\ 1 &amp; 3 &amp; -1 &amp; 2 \\ -1 &amp; -3 &amp; 2 &amp; 0 \end{array}\right].</me>
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Mark the position where the first pivot should be.
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Which row operation is the best choice for the first move in converting to RREF?
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</p>
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<ol marker="A.">
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<li> Add row 1 to row 2 (<m>R_2+R_1 \rightarrow R_2</m>)
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</li>
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<li> Add -1 row 3 to row 2 (<m>R_2-R_3 \rightarrow R_2</m>)
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</li>
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<li> Add -1 row 2 to row 3 (<m>R_3-R_2 \rightarrow R_3</m>)
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</li>
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<li> Add row 2 to row 1 (<m>R_1+R_2 \rightarrow R_1</m>)
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</li>
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</ol>
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</statement>
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<ol marker="A.">
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<li> Add row 3 to row 2 (<m>R_2+R_3 \rightarrow R_2</m>)
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</li>
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<li> Add row 2 to row 3 (<m>R_3+R_2 \rightarrow R_3</m>)
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</li>
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<li> Swap row 1 to row 2 (<m>R_1 \leftrightarrow R_2</m>)
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</li>
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<li> Add -2 row 2 to row 1 (<m>R_1-2R_2 \rightarrow R_1</m>)
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</li>
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</ol>
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</task>
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</activity>
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<observation>

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