Section 3.7 Solving Systems of Linear Equations by Using Matrices 297 Solving a System by Using the Gauss-Jordan Method Solve by using the Gauss-Jordan method. x y 5 2x 2z y 10 Solution: First write each equation in the system in standard form. x y 5 x y 5 2x 2z y 10 2x y 2z 10 3x 6y 7z 14 3x 6y 7z 14 2R1 R2 1 R2 3R1 R3 1 R3 £ 1 1 0 2 1 2 3 6 7 † 5 10 14 § 3x 6y 7z 14 Example 5 Set up the augmented matrix. Multiply row 1 by 2 and add the result to row 2. Multiply row 1 by 3 and add the result to row 3. £ 1 1 0 0 1 2 0 3 7 † 5 0 1 § Answer 11. 511, 1, 226 1R2 R1 1 R1 3R2 R3 1 R3 2R3 R1 1 R1 From the reduced row echelon form of the matrix, we have and The solution set is {(3, 2,1)}. z 1. Skill Practice Solve by using the Gauss-Jordan method. 11. x y z 2 x y z 4 x 4y 2z 1 x 3, y 2, 2R3 R2 1 R2 £ 1 0 0 0 1 0 0 0 1 † 3 2 1 § £ 1 0 2 0 1 2 0 0 1 † 5 0 1 § Multiply row 2 by 1 and add the result to row 1. Multiply row 2 by 3 and add the result to row 3. Multiply row 3 by 2 and add the result to row 1. Multiply row 3 by 2 and add the result to row 2.
miller_intermediate_algebra_4e_ch1_3
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