Educational calculation tool rather than \"question\".
\nThis allows the student to input a square matrix (max rows 5). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the matrix and the identity matrix (or what it has got to). This question has no marks and no feedback as it's just meant as a \"calculator\". It has some checks in so students know when they are not entering a square matrix or a valid row number etc.
\nIt has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.
\nIt would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Type in a matrix you would like to use the inverse algorithm on, and then say which row operations you would like to do. These will then be calculated for you, on the matrix and on the identity matrix next to it. You can choose the size of your matrix: in this implementation only up to 5 rows/columns.
\nAs there are no \"correct answers\", nothing will be marked, but you will have to submit each part in order to continue. If you click on \"reveal answers\", you will see all steps you have gone through listed (you may have to click back in the menu). You can use the navigation at the top to go back to previous parts if you want to take a different route.
", "advice": "You can see all your steps above. You may have to click back through the parts in the menu.
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"matrix_A": {"name": "matrix_A", "group": "the system", "definition": "matrix([0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0])", "description": "Matrix that will take the values of what the students enter for their linear system. This is just the side on the left: augmentation vector is separate.
", "templateType": "anything", "can_override": false}, "augmentation_b": {"name": "augmentation_b", "group": "the system", "definition": "id(5)", "description": "This will be the right hand side of the algorithm, starting off with the identity matrix. It will update from the student's calculation steps.
", "templateType": "anything", "can_override": false}, "row1multiplier": {"name": "row1multiplier", "group": "Calculating mutiples of rows", "definition": "1", "description": "number to multiply row 1 by.
", "templateType": "anything", "can_override": false}, "row2multiplier": {"name": "row2multiplier", "group": "Calculating mutiples of rows", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "row3multiplier": {"name": "row3multiplier", "group": "Calculating mutiples of rows", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "row4multiplier": {"name": "row4multiplier", "group": "Calculating mutiples of rows", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "row5multiplier": {"name": "row5multiplier", "group": "Calculating mutiples of rows", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "first_row_being_changed": {"name": "first_row_being_changed", "group": "Calculating row additions", "definition": "2", "description": "", "templateType": "anything", "can_override": false}, "second_row_being_changed": {"name": "second_row_being_changed", "group": "Calculating row additions", "definition": "3", "description": "", "templateType": "anything", "can_override": false}, "third_row_being_changed": {"name": "third_row_being_changed", "group": "Calculating row additions", "definition": "4", "description": "", "templateType": "anything", "can_override": false}, "fourth_row_being_changed": {"name": "fourth_row_being_changed", "group": "Calculating row additions", "definition": "5", "description": "", "templateType": "anything", "can_override": false}, "lambda1": {"name": "lambda1", "group": "Calculating row additions", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "lambda2": {"name": "lambda2", "group": "Calculating row additions", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "lambda3": {"name": "lambda3", "group": "Calculating row additions", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "lambda4": {"name": "lambda4", "group": "Calculating row additions", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "remultiplied_A": {"name": "remultiplied_A", "group": "Calculating mutiples of rows", "definition": "precround(switch(numrows(matrix_A)=1,matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0]),\n numrows(matrix_A)=2,matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0],if(isnan(row2multiplier),1,row2multiplier)*matrix_A[1]),\n numrows(matrix_A)=3,matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0],if(isnan(row2multiplier),1,row2multiplier)*matrix_A[1],if(isnan(row3multiplier),1,row3multiplier)*matrix_A[2]),\n numrows(matrix_A)=4,matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0],if(isnan(row2multiplier),1,row2multiplier)*matrix_A[1],if(isnan(row3multiplier),1,row3multiplier)*matrix_A[2],if(isnan(row4multiplier),1,row4multiplier)*matrix_A[3]),\n numrows(matrix_A)=5,matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0],if(isnan(row2multiplier),1,row2multiplier)*matrix_A[1],if(isnan(row3multiplier),1,row3multiplier)*matrix_A[2],if(isnan(row4multiplier),1,row4multiplier)*matrix_A[3],if(isnan(row5multiplier),1,row5multiplier)*matrix_A[4]),\n matrix(if(isnan(row1multiplier),1,row1multiplier)*matrix_A[0],if(isnan(row2multiplier),1,row2multiplier)*matrix_A[1],if(isnan(row3multiplier),1,row3multiplier)*matrix_A[2],if(isnan(row4multiplier),1,row4multiplier)*matrix_A[3],if(isnan(row5multiplier),1,row5multiplier)*matrix_A[4])),13)", "description": "changed matrix A after multiplying rows. It takes into account possible different sizes of the matrix. Up to 5 rows.
", "templateType": "anything", "can_override": false}, "remultiplied_b": {"name": "remultiplied_b", "group": "Calculating mutiples of rows", "definition": "precround(switch(numrows(augmentation_b)=1,matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0]),\n numrows(augmentation_b)=2,matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0],if(isnan(row2multiplier),1,row2multiplier)*augmentation_b[1]),\n numrows(augmentation_b)=3,matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0],if(isnan(row2multiplier),1,row2multiplier)*augmentation_b[1],if(isnan(row3multiplier),1,row3multiplier)*augmentation_b[2]),\n numrows(augmentation_b)=4,matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0],if(isnan(row2multiplier),1,row2multiplier)*augmentation_b[1],if(isnan(row3multiplier),1,row3multiplier)*augmentation_b[2],if(isnan(row4multiplier),1,row4multiplier)*augmentation_b[3]),\n numrows(augmentation_b)=5,matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0],if(isnan(row2multiplier),1,row2multiplier)*augmentation_b[1],if(isnan(row3multiplier),1,row3multiplier)*augmentation_b[2],if(isnan(row4multiplier),1,row4multiplier)*augmentation_b[3],if(isnan(row5multiplier),1,row5multiplier)*augmentation_b[4]),\n matrix(if(isnan(row1multiplier),1,row1multiplier)*augmentation_b[0],if(isnan(row2multiplier),1,row2multiplier)*augmentation_b[1],if(isnan(row3multiplier),1,row3multiplier)*augmentation_b[2],if(isnan(row4multiplier),1,row4multiplier)*augmentation_b[3],if(isnan(row5multiplier),1,row5multiplier)*augmentation_b[4])),13)", "description": "changed augmentation b after multiplying rows. It takes into account possible different sizes of the matrix. Up to 5 rows.
", "templateType": "anything", "can_override": true}, "readded_A_row1": {"name": "readded_A_row1", "group": "Calculating row additions", "definition": "switch(row_being_added=1,adding_step[0],first_row_being_changed=1,adding_step[1],second_row_being_changed=1,adding_step[2],third_row_being_changed=1,adding_step[3],fourth_row_being_changed=1,adding_step[4],matrix_A[0])", "description": "", "templateType": "anything", "can_override": false}, "adding_step": {"name": "adding_step", "group": "Calculating row additions", "definition": "matrix(matrix_A[row_being_added-1],matrix_A[first_row_being_changed-1]+lambda1*matrix_A[row_being_added-1],matrix_A[second_row_being_changed-1]+lambda2*matrix_A[row_being_added-1],matrix_A[third_row_being_changed-1]+lambda3*matrix_A[row_being_added-1],matrix_A[fourth_row_being_changed-1]+lambda4*matrix_A[row_being_added-1])", "description": "recalculating the rows of the matrix, but they are now potentially in the wrong order.
", "templateType": "anything", "can_override": false}, "row_being_added": {"name": "row_being_added", "group": "Calculating row additions", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "readded_A_row2": {"name": "readded_A_row2", "group": "Calculating row additions", "definition": "switch(row_being_added=2,adding_step[0],first_row_being_changed=2,adding_step[1],second_row_being_changed=2,adding_step[2],third_row_being_changed=2,adding_step[3],fourth_row_being_changed=2,adding_step[4],matrix_A[1])", "description": "", "templateType": "anything", "can_override": false}, "readded_A_row3": {"name": "readded_A_row3", "group": "Calculating row additions", "definition": "switch(row_being_added=3,adding_step[0],first_row_being_changed=3,adding_step[1],second_row_being_changed=3,adding_step[2],third_row_being_changed=3,adding_step[3],fourth_row_being_changed=3,adding_step[4],matrix_A[2])", "description": "", "templateType": "anything", "can_override": false}, "readded_A_row4": {"name": "readded_A_row4", "group": "Calculating row additions", "definition": "switch(row_being_added=4,adding_step[0],first_row_being_changed=4,adding_step[1],second_row_being_changed=4,adding_step[2],third_row_being_changed=4,adding_step[3],fourth_row_being_changed=4,adding_step[4],matrix_A[3])", "description": "", "templateType": "anything", "can_override": false}, "readded_A_row5": {"name": "readded_A_row5", "group": "Calculating row additions", "definition": "switch(row_being_added=5,adding_step[0],first_row_being_changed=5,adding_step[1],second_row_being_changed=5,adding_step[2],third_row_being_changed=5,adding_step[3],fourth_row_being_changed=5,adding_step[4],matrix_A[4])", "description": "", "templateType": "anything", "can_override": false}, "readded_A": {"name": "readded_A", "group": "Calculating row additions", "definition": "precround(switch(numrows(matrix_A)=1,matrix(readded_A_row1),\n numrows(matrix_A)=2,matrix(readded_A_row1,readded_A_row2),\n numrows(matrix_A)=3,matrix(readded_A_row1,readded_A_row2,readded_A_row3),\n numrows(matrix_A)=4, matrix(readded_A_row1,readded_A_row2,readded_A_row3,readded_A_row4),\n numrows(matrix_A)=5, matrix(readded_A_row1,readded_A_row2,readded_A_row3,readded_A_row4,readded_A_row5),\n matrix(readded_A_row1,readded_A_row2,readded_A_row3,readded_A_row4,readded_A_row5)),13)", "description": "Putting together the new rows of matrix A in the right order after some row additions. Takes into account different sizes.
", "templateType": "anything", "can_override": false}, "readded_b": {"name": "readded_b", "group": "Calculating row additions", "definition": "precround(switch(numrows(augmentation_b)=1, matrix(readded_b_row1),\n numrows(augmentation_b)=2,matrix(readded_b_row1,readded_b_row2),\n numrows(augmentation_b)=3, matrix(readded_b_row1,readded_b_row2,readded_b_row3),\n numrows(augmentation_b)=4, matrix(readded_b_row1,readded_b_row2,readded_b_row3,readded_b_row4),\n numrows(augmentation_b)=5,matrix(readded_b_row1,readded_b_row2,readded_b_row3,readded_b_row4,readded_b_row5),\n matrix(readded_b_row1,readded_b_row2,readded_b_row3,readded_b_row4,readded_b_row5)),13)", "description": "Putting together the new rows of augmentation b in the right order after some row additions. Takes into account different sizes.
", "templateType": "anything", "can_override": false}, "adding_step_b": {"name": "adding_step_b", "group": "Calculating row additions", "definition": "matrix(augmentation_b[row_being_added-1],augmentation_b[first_row_being_changed-1]+lambda1*augmentation_b[row_being_added-1],augmentation_b[second_row_being_changed-1]+lambda2*augmentation_b[row_being_added-1],augmentation_b[third_row_being_changed-1]+lambda3*augmentation_b[row_being_added-1],augmentation_b[fourth_row_being_changed-1]+lambda4*augmentation_b[row_being_added-1])", "description": "", "templateType": "anything", "can_override": false}, "readded_b_row1": {"name": "readded_b_row1", "group": "Calculating row additions", "definition": "switch(row_being_added=1,adding_step_b[0],first_row_being_changed=1,adding_step_b[1],second_row_being_changed=1,adding_step_b[2],third_row_being_changed=1,adding_step_b[3],fourth_row_being_changed=1,adding_step_b[4],augmentation_b[0])", "description": "", "templateType": "anything", "can_override": false}, "readded_b_row2": {"name": "readded_b_row2", "group": "Calculating row additions", "definition": "switch(row_being_added=2,adding_step_b[0],first_row_being_changed=2,adding_step_b[1],second_row_being_changed=2,adding_step_b[2],third_row_being_changed=2,adding_step_b[3],fourth_row_being_changed=2,adding_step_b[4],augmentation_b[1])", "description": "", "templateType": "anything", "can_override": false}, "readded_b_row3": {"name": "readded_b_row3", "group": "Calculating row additions", "definition": "switch(row_being_added=3,adding_step_b[0],first_row_being_changed=3,adding_step_b[1],second_row_being_changed=3,adding_step_b[2],third_row_being_changed=3,adding_step_b[3],fourth_row_being_changed=3,adding_step_b[4],augmentation_b[2])", "description": "", "templateType": "anything", "can_override": false}, "readded_b_row4": {"name": "readded_b_row4", "group": "Calculating row additions", "definition": "switch(row_being_added=4,adding_step_b[0],first_row_being_changed=4,adding_step_b[1],second_row_being_changed=4,adding_step_b[2],third_row_being_changed=4,adding_step_b[3],fourth_row_being_changed=4,adding_step_b[4],augmentation_b[3])", "description": "", "templateType": "anything", "can_override": false}, "readded_b_row5": {"name": "readded_b_row5", "group": "Calculating row additions", "definition": "switch(row_being_added=5,adding_step_b[0],first_row_being_changed=5,adding_step_b[1],second_row_being_changed=5,adding_step_b[2],third_row_being_changed=5,adding_step_b[3],fourth_row_being_changed=5,adding_step_b[4],augmentation_b[4])", "description": "", "templateType": "anything", "can_override": false}, "new1strow": {"name": "new1strow", "group": "Switching rows", "definition": "1", "description": "For switching rows.
", "templateType": "anything", "can_override": false}, "new2ndrow": {"name": "new2ndrow", "group": "Switching rows", "definition": "2", "description": "", "templateType": "anything", "can_override": false}, "new3rdrow": {"name": "new3rdrow", "group": "Switching rows", "definition": "3", "description": "", "templateType": "anything", "can_override": false}, "new5throw": {"name": "new5throw", "group": "Switching rows", "definition": "5", "description": "", "templateType": "anything", "can_override": false}, "new4throw": {"name": "new4throw", "group": "Switching rows", "definition": "4", "description": "", "templateType": "anything", "can_override": false}, "swapped_rows_A": {"name": "swapped_rows_A", "group": "Switching rows", "definition": "switch(numrows(matrix_A)=1, matrix(matrix_A[0]),\n numrows(matrix_A)=2,matrix(matrix_A[if(isnan(new1strow),1,new1strow)-1],matrix_A[if(isnan(new2ndrow),2,new2ndrow)-1]),\n numrows(matrix_A)=3,matrix(matrix_A[if(isnan(new1strow),1,new1strow)-1],matrix_A[if(isnan(new2ndrow),2,new2ndrow)-1],matrix_A[if(isnan(new3rdrow),3,new3rdrow)-1]),\n numrows(matrix_A)=4, matrix(matrix_A[if(isnan(new1strow),1,new1strow)-1],matrix_A[if(isnan(new2ndrow),2,new2ndrow)-1],matrix_A[if(isnan(new3rdrow),3,new3rdrow)-1],matrix_A[if(isnan(new4throw),4,new4throw)-1]),\n numrows(matrix_A)=5,matrix(matrix_A[if(isnan(new1strow),1,new1strow)-1],matrix_A[if(isnan(new2ndrow),2,new2ndrow)-1],matrix_A[if(isnan(new3rdrow),3,new3rdrow)-1],matrix_A[if(isnan(new4throw),4,new4throw)-1],matrix_A[if(isnan(new5throw),5,new5throw)-1]),\n matrix(matrix_A[if(isnan(new1strow),1,new1strow)-1],matrix_A[if(isnan(new2ndrow),2,new2ndrow)-1],matrix_A[if(isnan(new3rdrow),3,new3rdrow)-1],matrix_A[if(isnan(new4throw),4,new4throw)-1],matrix_A[if(isnan(new5throw),5,new5throw)-1]))", "description": "New matrix after swapping rows around.
", "templateType": "anything", "can_override": false}, "swapped_rows_b": {"name": "swapped_rows_b", "group": "Switching rows", "definition": "switch(numrows(augmentation_b)=1, matrix(augmentation_b[0]),\n numrows(augmentation_b)=2,matrix(augmentation_b[if(isnan(new1strow),1,new1strow)-1],augmentation_b[if(isnan(new2ndrow),2,new2ndrow)-1]),\n numrows(augmentation_b)=3,matrix(augmentation_b[if(isnan(new1strow),1,new1strow)-1],augmentation_b[if(isnan(new2ndrow),2,new2ndrow)-1],augmentation_b[if(isnan(new3rdrow),3,new3rdrow)-1]),\n numrows(augmentation_b)=4, matrix(augmentation_b[if(isnan(new1strow),1,new1strow)-1],augmentation_b[if(isnan(new2ndrow),2,new2ndrow)-1],augmentation_b[if(isnan(new3rdrow),3,new3rdrow)-1],augmentation_b[if(isnan(new4throw),4,new4throw)-1]),\n numrows(augmentation_b)=5,matrix(augmentation_b[if(isnan(new1strow),1,new1strow)-1],augmentation_b[if(isnan(new2ndrow),2,new2ndrow)-1],augmentation_b[if(isnan(new3rdrow),3,new3rdrow)-1],augmentation_b[if(isnan(new4throw),4,new4throw)-1],augmentation_b[if(isnan(new5throw),5,new5throw)-1]),\n matrix(augmentation_b[if(isnan(new1strow),1,new1strow)-1],augmentation_b[if(isnan(new2ndrow),2,new2ndrow)-1],augmentation_b[if(isnan(new3rdrow),3,new3rdrow)-1],augmentation_b[if(isnan(new4throw),4,new4throw)-1],augmentation_b[if(isnan(new5throw),5,new5throw)-1]))", "description": "", "templateType": "anything", "can_override": false}, "original_A": {"name": "original_A", "group": "Ungrouped variables", "definition": "matrix([0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0],[0,0,0,0,0])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["original_A"], "variable_groups": [{"name": "the system", "variables": ["matrix_A", "augmentation_b"]}, {"name": "Calculating mutiples of rows", "variables": ["row1multiplier", "row2multiplier", "row3multiplier", "row4multiplier", "row5multiplier", "remultiplied_A", "remultiplied_b"]}, {"name": "Calculating row additions", "variables": ["row_being_added", "first_row_being_changed", "second_row_being_changed", "third_row_being_changed", "fourth_row_being_changed", "lambda1", "lambda2", "lambda3", "lambda4", "adding_step", "readded_A_row1", "readded_A_row2", "readded_A_row3", "readded_A_row4", "readded_A_row5", "readded_A", "adding_step_b", "readded_b_row1", "readded_b_row2", "readded_b_row3", "readded_b_row4", "readded_b_row5", "readded_b"]}, {"name": "Switching rows", "variables": ["new1strow", "new2ndrow", "new3rdrow", "new4throw", "new5throw", "swapped_rows_A", "swapped_rows_b"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Enter matrix", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "\nmark:\n apply(gap_feedback);\n assert(all_valid , fail(translate(\"question.can not submit\")));\n apply(answers)\n \n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Multiply some rows", "rawLabel": "", "otherPart": 3, "variableReplacements": [{"variable": "augmentation_b", "definition": "id(numrows(interpreted_answer[0]))"}, {"variable": "matrix_A", "definition": "interpreted_answer[0]"}, {"variable": "original_A", "definition": "interpreted_answer[0]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Add multiples of some row to other rows", "rawLabel": "", "otherPart": 1, "variableReplacements": [{"variable": "augmentation_b", "definition": "id(numrows(interpreted_answer[0]))"}, {"variable": "matrix_A", "definition": "interpreted_answer[0]"}, {"variable": "original_A", "definition": "interpreted_answer[0]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Swap some rows", "rawLabel": "", "otherPart": 5, "variableReplacements": [{"variable": "augmentation_b", "definition": "id(numrows(interpreted_answer[0]))"}, {"variable": "matrix_A", "definition": "interpreted_answer[0]"}, {"variable": "original_A", "definition": "interpreted_answer[0]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}, {"label": "Finish", "rawLabel": "", "otherPart": 7, "variableReplacements": [{"variable": "augmentation_b", "definition": "id(numrows(interpreted_answer[0]))"}, {"variable": "matrix_A", "definition": "interpreted_answer[0]"}, {"variable": "original_A", "definition": "interpreted_answer[0]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Enter your matrix which you want to apply the inverse algorithm to. It needs to be a square matrix. The identity matrix of the same size will be added automatically in the next step for your calculations.
\n[[0]]
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\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b} \\right.\\]
\nEnter what you would like to calculate. You can choose one row to add to one or more of the other rows. The entries in front of \"times\" can be fractions. You can leave blank any entries you don't need.
\nYou matrix only has one row, so there is no valid \"add a multiple of one row to another row\" operation.
\nAdd [[0]] times row [[1]] to row [[2]].
Add [[3]] times row [[1]] to row [[4]].
Add [[5]] times row [[1]] to row [[6]].
Add [[7]] times row [[1]] to row [[8]].
You have gone from
\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b}\\right.\\qquad \\text{to} \\qquad \\left.\\var[fractionNumbers]{readded_A} \\middle| \\var[fractionNumbers]{readded_b}\\right.\\]
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\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b} \\right.\\]
\nEnter what you would like to calculate. You can enter fractions if you want. You can leave blank any entries you don't need (if you want that row to stay as it is).
\n[[0]] times row 1.
[[1]] times row 2.
[[2]] times row 3.
[[3]] times row 4.
[[4]] times row 5.
You have gone from
\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b}\\right.\\qquad \\text{to} \\qquad\\left. \\var[fractionNumbers]{remultiplied_A} \\middle| \\var[fractionNumbers]{remultiplied_b}\\right.\\]
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\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b} \\right.\\]
\nEnter which rows you want to swap. So as not to lose information, make sure you don't enter any row number twice!
\nYou only have one row, so you can't swap any rows.
\nOld row [[0]] becomes new row 1.
Old row [[1]] becomes new row 2.
Old row [[2]] becomes new row 3.
Old row [[3]] becomes new row 4.
Old row [[4]] becomes new row 5.
You have gone from
\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b}\\right.\\qquad \\text{to} \\qquad\\left. \\var[fractionNumbers]{swapped_rows_A} \\middle| \\var[fractionNumbers]{swapped_rows_b}\\right.\\]
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\n\\[ \\left. \\var[fractionNumbers]{matrix_A} \\middle| \\var[fractionNumbers]{augmentation_b}\\right.\\]
\nYour original matrix times the right-hand side is:
\n\\[\\var[fractionNumbers]{original_A}\\var[fractionNumbers]{augmentation_b}=\\var[fractionNumbers]{original_A*augmentation_b}\\]
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