294 Chapter 3 Systems of Linear Equations and Inequalities If we extract both the coefficients and the constants from the equations, we can construct the augmented matrix of the system: 5 5 A vertical bar is inserted into an augmented matrix to designate the position of the equal signs. Writing an Augmented Matrix for a System of Linear Equations Write the augmented matrix for each linear system. a. 3x 4y 3 b. 2x 3z 14 2x 4y 2 2y z 2 Solution: c3 4 § 3 2 a. b. 14 2 4 Skill Practice Write the augmented matrix for each system. 5. x y 4 6. 2x y z 14 2x y 1 3x 4y 8 x y 5z 0 £ 2 0 3 0 2 1 1 1 0 † 2 4 ` d x y 4 Example 2 c 2 1 1 2 ` d TIP: Notice that zeros are inserted to denote the coefficient of each missing term. Writing a Linear System from an Augmented Matrix Write a system of linear equations represented by each augmented matrix. 14 5 2 c 2 5 § 4 1 £ § 8 6 a. b. c. Solution: a. b. c. 2x 5y 8 2x y 3z 14 4x y 6 x y 2z 5 x 0y 0z 4 x 4 0x y 0z 1 or y 1 0x 0y z 0 z 0 Skill Practice Write a system of linear equations represented by each augmented matrix. 7. 8. 9. c § 2 3 1 8 4 20 6 £ £ § 1 0 0 0 1 0 0 0 1 8 2 15 † 3 2 1 14 1 0 8 3 5 † 5 1 ` d 3x y z 2 £ 1 0 0 0 1 0 0 0 1 4 1 0 † 2 1 3 1 1 2 3 1 1 † ` d Example 3 Answers 5. 6. 7. 8. c1 1 2 1 4 1 ` 2 1 1 3 4 0 1 1 5 £ 2x 3y 5 x 8y 1 14 8 0 d † § 3x 2y z 4 14x y 20 8x 3y 5z 6 9. x 8, y 2, z 15
miller_intermediate_algebra_4e_ch1_3
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