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7.4C Gauss-Jordan Elimination. Guass -Jordan Elimination : Creates a matrix in REDUCED ROW ECHELON FORM . (Use row operations) Row Echelon form Rows with all zeros are at bottom First non-zero entry in each row is a 1
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7.4C Gauss-Jordan Elimination • Guass-Jordan Elimination: Creates a matrix in REDUCED ROW ECHELON FORM. (Use row operations) • Row Echelon form • Rows with all zeros are at bottom • First non-zero entry in each row is a 1 • The leading 1 in the previous row is always farther to the left than the current row. • Every column with a leading 1 has ZEROS in every location both ABOVE AND BELOW it. • Solutions are values on the Right side
Examples: Give the solution • 1. • 2.
Hints for turning Gauss in to Gauss Jordan • Once you have already created ROW ECHELON FORM with Gauss elimination: Make zeros in counter-clockwise fashion. (3x3) • 1. ) Create ZEROS in column above leading 1 in LAST ROW • Make opposites with the 1 and the number above it, add and replace second row, repeat with top row. • 2) Create ZEROS in column above leading 1 in second row • Make opposites with the 1 in second row and number above it, add and replace top row.
