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o] 10. 7 3x + 2y || 5 -7 3 21 -9 -15 17 50

o] 10. 7 3x + 2y || 5 -7 3 21 -9 -15 17 50

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Number 10

1-14 GAUSS ELIMINATION Solve the linear system given explicitly or by its augmented matrix. Show details. 1. 4x6y=-11 3. 5. 7. 9. 11. - 3x + 8y 9 8y + 6z = -6 -2x + 4y - 6z = 40 13 12 -6 -4 7 -73 157 11 x + y = 2 = 2 -1 4 4 10 - 13 4 1 0 6 -2y2z = -8 3x + 4y - 5z = 13 0 5 5 -10 -3 -3 1 1 Z = 1 0 -2 0 0 6 2. [3.0 4. 6. 8. 10. 0 2 -2 4 1.5 4 5 -9 4 -1 3 5 -0.5 4.5 1 -15 -3 2x 3x + 2y -8 0 1 0.6 2 -5 6.0 2 -1 5 3 16 -21 -6 1 4y + 3z = 8 z = 2 = 5 4 -7 3 21 -9 2 7 17 50 12. 13. 14. -3 1 2 -2 4 3 -6 -3w 2 w + 8w 3 -1 2 10x + 4y 17x + x + y 34x + 16y 3 1 5 3 -7 y + 0 5 0 - 11 10z = 1 5 -2 5 1 - 1 3 4 2 -7 15. Equivalence relation. By definition, an equivalence relation on a set is a relation satisfying three conditions: (named as indicated) (i) Each element A of the set is equivalent to itself (Reflexivity). (ii) If A is equivalent to B, then B is equivalent to A (Symmetry). 0 15 –4 -3 2z = 2z = = 0 -4 2 6 4 (iii) If A is equivalent to B and B is equivalent to C, then A is equivalent to C (Transitivity). Show that row equivalence of matrices satisfies these three conditions. Hint. Show that for each of the three elementary row operations these conditions hold.
Transcribed Image Text:1-14 GAUSS ELIMINATION Solve the linear system given explicitly or by its augmented matrix. Show details. 1. 4x6y=-11 3. 5. 7. 9. 11. - 3x + 8y 9 8y + 6z = -6 -2x + 4y - 6z = 40 13 12 -6 -4 7 -73 157 11 x + y = 2 = 2 -1 4 4 10 - 13 4 1 0 6 -2y2z = -8 3x + 4y - 5z = 13 0 5 5 -10 -3 -3 1 1 Z = 1 0 -2 0 0 6 2. [3.0 4. 6. 8. 10. 0 2 -2 4 1.5 4 5 -9 4 -1 3 5 -0.5 4.5 1 -15 -3 2x 3x + 2y -8 0 1 0.6 2 -5 6.0 2 -1 5 3 16 -21 -6 1 4y + 3z = 8 z = 2 = 5 4 -7 3 21 -9 2 7 17 50 12. 13. 14. -3 1 2 -2 4 3 -6 -3w 2 w + 8w 3 -1 2 10x + 4y 17x + x + y 34x + 16y 3 1 5 3 -7 y + 0 5 0 - 11 10z = 1 5 -2 5 1 - 1 3 4 2 -7 15. Equivalence relation. By definition, an equivalence relation on a set is a relation satisfying three conditions: (named as indicated) (i) Each element A of the set is equivalent to itself (Reflexivity). (ii) If A is equivalent to B, then B is equivalent to A (Symmetry). 0 15 –4 -3 2z = 2z = = 0 -4 2 6 4 (iii) If A is equivalent to B and B is equivalent to C, then A is equivalent to C (Transitivity). Show that row equivalence of matrices satisfies these three conditions. Hint. Show that for each of the three elementary row operations these conditions hold.
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