Row Reduction/Solving Linear Systems
with the LinearSolveTutor(Menu: Tools, Tutors, Linear Algebra, Solving Linear Systems, Pick Gauss-Jordan)
You have 4 choices to enter a matrix (the tutor only allows you to edit up to 5 rows or columns):
1) with the Matrix palette,
2) with the Matrix command,
3) or with the shortcut < | ,> notation, with " | " as a horizontal separator, and " , " as a vertical separator, either by rows or columns:
This line has to be executed to access the reduction and backsubstitution commands. A colon its end suppresses the listing of commands it loads:QyQtSSV3aXRoRzYiNiMmSShTdHVkZW50R0koX3N5c2xpYkdGJTYjSS5MaW5lYXJBbGdlYnJhRzYkJSpwcm90ZWN0ZWRHRikhIiI=PkkiQUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjL0kkJWlkR0YkIiopRyRSXyI=PkkiQUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjNyU3JiIiJCIiKSIiKCIjPzcmIiIiIiIjRjIiIiU3JkYzRi8iIioiI0I=PkkiQUc2Ii1JJDwsPkdGJDYlLUkkPHxncj5HRiQ2JiIiJCIiKSIiKCIjPy1GKTYmIiIiIiIjRjEiIiUtRik2JkYyRi0iIioiI0I=PkkiQUc2Ii1JJDx8Z3I+R0koX3N5c2xpYkdGJDYmLUkkPCw+R0YnNiUiIiQiIiIiIiMtRio2JSIiKUYuIiIoLUYqNiVGMkYtIiIqLUYqNiUiIz8iIiUiI0I=If you just type in "Red" and then hit the autocomplete key combination Cntrl Space, it will put in the rest of the command, so you don't have to remember more than the first 3 letters, case sensitive. The same is true of "Back" plus autocomplete (you have to choose from two possibilities).QyUtSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HNiI2I0kiQUdGJSIiIi1JM0JhY2t3YXJkU3Vic3RpdHV0ZUdGJTYjSSIlR0YlThere are two tutors accessible directly from the Tools Menu, Tutors, Linear Algebra: Gauss-Jordan Elimination or Solving Linear Systems, but they are restricted to at most 5x5 matrices. If the Student[LinearAlgebra] package is loaded, they can be accessed by the commands GaussJordanEliminationTutor and LinearSolveTutor with a preloaded matrix already defined. The LinearSolveTutor allows first the matrix reduction and then the solution of the associated linear system of equations for which that matrix is the augmented matrix. Here is an example:LUkxTGluZWFyU29sdmVUdXRvckc2IjYjSSJBR0Yktransferring from the tutor windows back into the worksheetIf you want to record both the reduction steps and the backsub solution from the tutor windows, you can open a second copy of Maple and mouse select Control C copy window contents in the Tutor one at a time to paste into a text region in the second worksheet and then copy and paste them all back into the original worksheet in a text region. Here I added some row operation notes to the reduction steps after each arrow, and copied both the equations and the solution as well: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
[When you execute the entire worksheet you get a Maple warning here and all this stuff echoed back, and then Maple does not seem to let you delete that extra junk easily. The first commands typed in after the arrows on each line are the actual row reduction commands one could use independent of the tutor, while the second annotation in row language is just shorthand. The AddRow(A,p,q,k) means for the matrix A add to row p the row q multiplied by k.]
Closing the tutor after solving the equations in the LinearSolveTutor gives you this output automatically:Equations: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: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Note that if you let Maple do all the steps, it will start by dividing by the upper left entry (it has no fear of fractions!)Now try this one step by step:PkkiQ0c2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjL0kkJWlkR0YkIiorKT5kPg==LUkxTGluZWFyU29sdmVUdXRvckc2IjYjSSJDR0YkThis is the matrix whose reduced form is given on the handout on solving linear systems:PkkiQ0c2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjL0kkJWlkR0YkIipvZGwxIw==QyUtSTZSZWR1Y2VkUm93RWNoZWxvbkZvcm1HNiI2I0kiQ0dGJSIiIi1JM0JhY2t3YXJkU3Vic3RpdHV0ZUdGJTYjSSIlR0YlNotice that here Maple assigns the parameter subscripts from bottom to top instead of from top to bottom. Makes no difference.JSFH