row reduction of augmented matrix
and solution of a linear systemUse the Matrix palette to insert matrices. Select dimensions, then use the tab key to cycle through the entries, overwriting the placeholders.
[The alternative is to insert the matrix inside the popup tutor.]LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvOpen Example 1 after executing the previous line to define the matrix.example 1: Gauss-Jordan Elimination Tutor (use for HW)
( 3x3 system example: 3x4 augmented matrix)The Gauss-Jordan Elimination Tutor exports all the steps, without continuing to the solution of the corresponding linear system BUT not for more than 5 columns. You can load this directly from the Tools, Tutor, LinearAlgebra choice when your cursor is in a blank input region and then close it to insert the symbol for the matrix in it, or insert the matrix inside the popup tutor.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoU3R1ZGVudEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNiQtRiw2JlEuTGluZWFyQWxnZWJyYUYnRi9GMkY1L0Y2USdub3JtYWxGJ0YyRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjk2Jy1GIzYkLUYsNiZRPEdhdXNzSm9yZGFuRWxpbWluYXRpb25UdXRvckYnRi9GMkY1RkBGMkZARkJGRS1GOTYlLUYjNiQtRiw2JVEiQ0YnRi9GNUZARjJGQC1GLDYjUSFGJ0YyRkA=Then choose Solvers and Forms, Linear Solve from the context menu here to get the solution of the corresponding 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Of course this is the RHS of the matrix solution equation (Copy and Paste and insert LHS):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example 2 with LinearSolveTutor, finishing the system solution
(3x5 system example: 3x6 augmented matrix)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 instead the LinearSolveTutor which allows more columns. It goes on to solve the system of equations represented by the augmented matrix.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: step by step reduction and solution with the Linear Solve TutorWe can use the Linear Solve Tutor in Maple to step by step row reduce the matrix.Go to the Tools menu, Tutors, Linear Algebra, Linear System Solving , and it will insert the command with empty parentheses at the end at the input line where the cursor is: > 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Then type in the name of the matrix already entered.
OR you can type the matrix directly into the popup window without first defining the matrix. First choose Edit Matrix and set the row and column numbers, then enter the entries and close out the Edit window. BUT this only allows from 2 to 5 columns unless you preload the wider matrix as indicated.
When you first enter the tutor, choose Gauss-Jordan Elimination instead of Gaussian Eimination (only partial reduction). Just quit this popup window and then insert "C" directly in the empty parentheses. Then after reducing the matrix, go on to Solve the System, and click in succession on Equations, Fee Variables, Solution.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEoU3R1ZGVudEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnRj0vJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjY2Ji1GIzYkLUYsNiVRMUxpbmVhclNvbHZlVHV0b3JGJ0YvRjJGPUY9Rj9GQi1GNjYkLUYjNiQtRiw2JVEiQ0YnRi9GMkY9Rj0tRiw2I1EhRidGPQ==This is the solution of the corresponding linear system with this augmented matrix (copied from the popup window), which is NOT output when you finish the Linear System Solving tutor.
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 the Maple Tutor returns only the column vector of the solution since there are no named variables associated with the matrix of numbers, that is for us to decide:
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 your results after learning the algorithmTo just check your augmented matrix reduction and the corresponding linear system solution in Maple:
Click on augmented matrix output entered with the Matrix palette, then from the context sensitive menu,
choose Solvers and Forms, Row Echelon Form, Reduced
to get the RREF form of the matrix.
Then choose Solvers and Forms, Linear Solve
to get the RHS of the solution of the corresponding linear system of equations.
Here are the results of selecting those two choices, applying the second to the first (or directly to the first).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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We can introduce our own variable names into this result as a 5x1 matrix using the Matrix 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