Classify the quadratic forms in Exercises 9-18. Then make a change of variable, x = Py, thatransforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. %3D 9. 4x - 4x1x2+ 4x3 10. 2x + 6x1x2-6x3 11. 2x-4x1x2 - x 12. -x- 2x1x2- x 13. x-6x1x2 + 9x 14. 3x +4x1x2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Classify the quadratic forms in Exercises 9-18. Then make a
change of variable, x = Py, thartransforms the quadratic form
into one with no cross-product term. Write the new quadratic form.
Construct P using the methods of Section 7.1.
9. 4x- 4x1x2 + 4x3
10. 2x + 6x1x2-6x3
11. 2x-4x1x2-x
12. –x} – 2x,x2 –- x3
13. x-6x1x2 + 9x
14. 3x +4x,X2
Transcribed Image Text:Classify the quadratic forms in Exercises 9-18. Then make a change of variable, x = Py, thartransforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 9. 4x- 4x1x2 + 4x3 10. 2x + 6x1x2-6x3 11. 2x-4x1x2-x 12. –x} – 2x,x2 –- x3 13. x-6x1x2 + 9x 14. 3x +4x,X2
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