900 CHAPTER 9 Systems and Matrices 3. What is the augmented matrix of the following system? -3x + 5y = 2 6 x + 2y = 7 4. By what number must the first row of the augmented matrix of Exercise 3 be multiplied so that when it is added to the second row, the element in the second row, first column becomes 0? 5. What is the augmented matrix of the following system? 3x + 2y = 5 -9x + 6z = 1 -8y + z = 4 6. By what number must the first row of the augmented matrix of Exercise 5 be multiplied so that when it is added to the second row, the element in the second row, first column becomes 0? Use the given row transformation to change each matrix as indicated. See Example 1. 7. c 1 4 4 7d ;4 times row 1 added to row 2 8. c 1 7 -4 0d ;7 times row 1 added to row 2 9. £ 1 -2 4 5 3 7 6 -1 0§; 2 times row 1 added to row 2 10. £ 1 -4 3 5 -1 7 6 2 1§; 4 times row 1 added to row 2 Concept Check Write the augmented matrix for each system and give its dimension. Do not solve. 11. 2x + 3y = 11 x + 2y = 8 12. 3x + 5y = -13 2x + 3y = -9 13. 2x + y + z - 3 = 0 3x - 4y + 2z + 7 = 0 x + y + z - 2 = 0 14. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0 Concept Check Write the system of equations associated with each augmented matrix. Do not solve. 15. £ 3 0 -1 2 2 -2 1 4 3 3 1 22 15§ 16. £ 2 4 5 1 -3 0 3 0 -4 3 12 10 -11§ 17. £ 1 0 0 0 1 0 0 0 1 3 2 3 -2§ 18. £ 1 0 0 0 1 0 0 0 1 3 4 2 3§ 19. 20.
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