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Unformatted text preview: 43 GaussJordan EliminationWe will do row operations:1. Interchange two rowsRiRj2. Multiply a rowby a constantcRiRi3. Add a multiple of one rowcRi+ RjRjto another•on an augmented matrix to solve a system•using a method known as GAUSSJORDANELIMINATION:1. Get a 1 in upper left corner (by row ops 1 and/or 2)2. Get 0's everywhere else in its column (by row op 3)3. Mentally delete row 1 and column 1. What remains is a smaller submatrix. 4. Get 1 in upper lefthand corner of the submatrix.5. Get 0's everywhere else in its column for all rowsin the matrix (not just the submatrix).6. Mentally delete row 1 and column 1 of the submatrix, forming an even smaller submatrix.7. Repeat 4, 5, 6 until you can go no further.8. The matrix will now be in reduced rowechelon form (RREF), or just reduced form.6. Rewrite the system in natural form.7. State the solution.A.If you get a row of all zeros, use row op 1 to make it the last rowB. If you get a row with all zeros to the left of the line, and a nonzero on the right, STOP (no solution)....
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff
 GaussJordan Elimination

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