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2. Gaussian Elimination GENERAL IDEA: 1. Forward Elimination 2. Back Substitution GOAL: Transform the system into Row-echelon form. HOW: Perform elementary row operations so that back substitution can be easily done. 3. Elementary Row Operations Changes done to a system of equations that still maintain its equivalence. There are only 3 Elementary Row Operations 1. Interchange 2 equations (or Rows) 2. Multiply one of the equations (or rows) by a non-zero constant. 3. Add a multiple of one row to another. 4. Gaussian Elimination Perform elementary row operations so that back substitution can be easily done. Suggested steps: 1. Obtain a coefficient of 1 for x in Row 1 2. Eliminate x from Row 2 and Row 3 3. Obtain a coefficient of 1 for y. 4. Eliminate y from Row 3 5. Obtain a coefficient of 1 for z then back substitute to solve.