300 Chapter 3 Systems of Linear Equations and Inequalities Concept 1: Introduction to Matrices For Exercises 6–14, (a) determine the order of each matrix and (b) determine if the matrix is a row matrix, a column matrix, a square matrix, or none of these. (See Example 1.) 5 1 2 ≥ § 6. 7. 8. c 3 9 34 74 30 8 11 54 1 3 9. 10. 11. 3 4 6 c 5 d 4.3 12. 13. 14. For Exercises 15–18, set up the augmented matrix. (See Example 2.) 15. 16. 17. 18. For Exercises 19–22, write a system of linear equations represented by the augmented matrix. (See Example 3.) 1 0 0 0 1 0 0 0 1 c 4 3 d 12 5 19. 20. 21. 22. Concept 2: Solving Systems of Linear Equations by Using the Gauss-Jordan Method £ 1 0 0 0 1 0 0 0 1 † 0.5 6.1 3.9 £ † § 4 1 7 c2 5 ` 15 § 7 15 45 ` 6 6 d 5x 17 2z 8x 6z 26 8x 3y 12z 24 y x 2y 5 z 2x 6y 3z 2 3x y 2z 1 x 3y 3 2x 5y 4 x 2y 1 2x y 7 £ 5 1 1 2 0 7 c § 13 2 1 78 8.1 9 4.2 18 0 3 d d £ 9 4 3 1 8 4 5 8 7 £ § 4 5 3 0 ¥ 23. Given the matrix E E c 3 2 9 1 a. What is the element in the second row and third column? b. What is the element in the first row and second column? ` 8 7 d 24. Given the matrix F a. What is the element in the second row and second column? b. What is the element in the first row and third column? F c1 8 12 13 ` 0 2 d 25. Given the matrix Z 12 write the matrix obtained by multiplying the elements in the first row by . Z c2 1 2 1 ` 11 1 d 26. Given the matrix J 13 write the matrix obtained by multiplying the elements in the second row by . J c1 1 0 3 ` 7 6 d 27. Given the matrix K K c5 2 1 4 ` 1 3 d write the matrix obtained by interchanging rows 1 and 2. 28. Given the matrix L L c 9 7 6 2 ` 13 19 d write the matrix obtained by interchanging rows 1 and 2.
miller_intermediate_algebra_4e_ch1_3
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