296 Chapter 3 Systems of Linear Equations and Inequalities Solving a System by Using the Gauss-Jordan Method Set up the augmented matrix. Switch row 1 and row 2 to get a 1 in the upper left position. Multiply row 1 by 2 and add the result to row 2. This produces an entry of 0 below the upper left position. Answer 10. 515, 826 Example 4 Solve by using the Gauss-Jordan method. 2x y 5 x 2y 5 C c1 0 ` ` 5 5 5 3 1 3 15 The matrix C is in reduced row echelon form. From the augmented matrix, we have and The solution set is {(1, 3)}. Skill Practice 10. Solve by using the Gauss-Jordan method. x 2y 21 2x y 2 x 1 y 3. 0 1 ` 1 3 d 2R2 R1 1 R1 c1 0 0 1 ` d 15 R2 1 R2 c1 2 0 1 ` d Multiply row 2 by to produce a 1 along the diagonal in the second row. Multiply row 2 by 2 and add the result to row 1.This produces a 0 in the first row, second column. Solution: 2R1 R2 1 R2 c1 2 0 5 5 15 d R13R2 c1 2 2 1 5 5 d c 2 1 1 2 ` d The order in which we manipulate the elements of an augmented matrix to produce reduced row echelon form was demonstrated in Example 4. In general, the order is as follows. • First produce a 1 in the first row, first column. Then use the first row to obtain 0’s in the first column below this element. • Next, if possible, produce a 1 in the second row, second column. Use the second row to obtain 0’s above and below this element. • Next, if possible, produce a 1 in the third row, third column. Use the third row to obtain 0’s above and below this element. • The process continues until reduced row echelon form is obtained.
miller_intermediate_algebra_4e_ch1_3
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