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Unformatted text preview: 4-3 Gauss-Jordan 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 GAUSS-JORDANELIMINATION: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 row-echelon form (RREF), or just reduced form.6. Re-write 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 non-zero 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
- Gauss-Jordan Elimination