915 9.3 Determinant Solution of Linear Systems CONCEPT PREVIEW Answer each question. 1. What is the value of 2 4 0 -2 02 ? 2. What is the value of 2 4 4 -2 -22 ? 3. What expression in x represents 2 x 4 3 x2 ? 4. What expression in x represents 2 4 3 x x2 ? 5. What is the value of x if 2 x 0 0 x2 = 9? 6. What is the value of x if 2 0 x x 02 = -4? 9.3 Exercises Evaluate each determinant. See Example 1. 7. 2 -5 4 9 -12 8. 2 -1 -2 3 92 9. 2 -1 5 -2 32 10. 2 6 0 -4 -12 11. 2 9 -3 3 -12 12. 2 0 1 2 52 13. 2 3 5 4 -22 14. 2 -9 2 7 62 15. 2 -7 3 0 02 16. Concept Check Refer to Exercise 11. Make a conjecture about the value of the determinant of a matrix in which one row is a multiple of another row. Find the cofactor of each element in the second row of each matrix. See Example 2. 17. C -2 1 4 0 2 2 1 0 1S 18. C 1 1 0 -1 0 -3 2 2 1S 19. C 1 2 -1 2 3 4 -1 -2 1S 20. C 2 3 -2 -1 0 1 4 1 4S 30. 3 5 -5 1 -3 3 0 2 -2 13 31. 3 1 0 0 0 1 0 0 0 13 32. 3 1 0 1 0 -1 0 0 0 13 Evaluate each determinant. See Example 3. 21. 3 4 2 -6 -7 1 3 8 3 03 22. 3 8 7 5 -2 0 -1 -4 3 23 23. 3 1 -1 0 2 2 1 0 -1 43 24. 3 2 4 2 1 7 4 -1 -2 03 25. 3 10 -1 -3 2 4 8 1 3 103 26. 3 7 1 -2 -1 -7 1 1 2 13 27. 3 1 0 1 -2 0 10 3 0 -123 28. 3 2 1 -1 3 9 -2 0 0 03 29. 3 3 2 -6 3 6 -6 -1 0 23
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