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7.4B- Gauss Elim . & Back Sub.

7.4B- Gauss Elim . & Back Sub. Elementary Row Operations for solving systems written as augmented matrices 1.) Interchange 2 rows 2.) Multiply (or divide) a row by a non-zero # 3.) Add a multiple of a row to another Multiply a row by a number Add to another row

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7.4B- Gauss Elim . & Back Sub.

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  1. 7.4B- Gauss Elim. & Back Sub. • Elementary Row Operations for solving systems written as augmented matrices • 1.) Interchange 2 rows • 2.) Multiply (or divide) a row by a non-zero # • 3.) Add a multiple of a row to another • Multiply a row by a number • Add to another row • Replace 1 of the 2 rows with the result

  2. Examples: Fill in blanks & tell row operations used • 1. → • 2. →

  3. Gauss-Elimination with Back Substitution • Turn linear system into augmented matrix • Apply Row Operations and create 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. • Turn matrix into linear system • Solve with back substitution

  4. Hints to creating row echelon form • Switch 2 row so R1 has leading coefficient = 1 • Make ZEROS in Column 1 • R1 & R2: opposites & add → R2 • R1 & R3: opposites & add → R3 • Continue until all # ‘s below are zeros • Divide R2 by lead coefficient to make “1” • Make Zeros below lead coefficient in C2 • R2 & R3: opposites add → R3 • R2 & R4: opposites & add → R4 • Continue until all #’s below are zeros • Divide R3 by lead coefficient to make “1” • Make Zeros below lead coefficient in C3 etc.

  5. Solve system with Gauss Elimination & Back Substitution • 3.

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