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# 4-3 - 4-3 Gauss-Jordan Elimination We will do row...

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4-3 Gauss-Jordan Elimination We will do row operations : 1. Interchange two rows R i  R j 2. Multiply a row by a constant cR i R i 3. Add a multiple of one row cR i + R j R j to another on an augmented matrix to solve a system using a method known as G AUSS -J ORDAN E LIMINATION : 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 rows in 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 row B.

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