Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 5.5, Problem 19EQ
To determine
To classify: The given quadratic form as positive definite, positive semidefinite, negative definite, negative semidefinite or indefinite.
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Chapter 5 Solutions
Linear Algebra: A Modern Introduction
Ch. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - Prob. 2EQCh. 5.1 - Prob. 3EQCh. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - Prob. 6EQCh. 5.1 - Prob. 7EQCh. 5.1 - Prob. 8EQCh. 5.1 - In Exercises 7-10, show that the given vectors...Ch. 5.1 - In Exercises 7-10, show that the given vectors...
Ch. 5.1 - Prob. 11EQCh. 5.1 - In Exercises 11-15, determine whether the given...Ch. 5.1 - In Exercises 11-15, determine whether the given...Ch. 5.1 - Prob. 14EQCh. 5.1 - Prob. 15EQCh. 5.1 - In Exercises 29-32, use Exercise 28 to determine...Ch. 5.1 - In Exercises 29-32, use Exercise 28 to determine...Ch. 5.2 - Prob. 15EQCh. 5.2 - In Exercises 15-18, find the orthogonal projection...Ch. 5.2 - Prob. 17EQCh. 5.2 - Prob. 18EQCh. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.5 - In Exercises 1-6, evaluate the quadratic form for...Ch. 5.5 - Prob. 2EQCh. 5.5 - Prob. 3EQCh. 5.5 - Prob. 4EQCh. 5.5 - Prob. 5EQCh. 5.5 - Prob. 6EQCh. 5.5 - Prob. 7EQCh. 5.5 - Prob. 8EQCh. 5.5 - Prob. 9EQCh. 5.5 - Prob. 10EQCh. 5.5 - In Exercises 7-12, find the symmetric matrix A...Ch. 5.5 - Prob. 12EQCh. 5.5 - Prob. 19EQCh. 5.5 - Classify each of the quadratic forms in Exercises...Ch. 5.5 - Prob. 21EQCh. 5.5 - Prob. 22EQCh. 5.5 - Prob. 23EQ
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- Determine the number and nature of the roots of the equation in Exercise 67. Calculate the discriminant associated with the equation 6x2+5x+1=0.arrow_forwardClassify 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,X2arrow_forwardUse quadratic formula to find all the real zeroes of the 2nd degree polynomials 6x²-x-1arrow_forward
- Find a simple quadratic with x = -1+ √2 as one of its solutions. Converting that simple quadratic to standard form, find the sum of the coefficients a + b + c.arrow_forwardIn Exercises3-4, classify the quadratic form as positive definite, negative definite, or positive semidefinite, negative semidefinite, or none of these? 3. q(x) = 2x² - 4x₁x₂ + 4x²/ 4. q(x) = 2x² + x² - 4x₁x2 - 4x2x3arrow_forwardThe subject of math is quadratics. Please complete in one sitting.arrow_forward
- Consider the quadratic equation: x2-4x+4=0a) Use the discriminant, b2-4ac, to determine the number of zeros of the quadratic function and their type (real or complex).b) Use a graph to verify the answer. Describe the graph and explain how it relates to the answer in part a.arrow_forwardConvert fO)=- x-6 X +4X-6 13D to factored form Ondarrow_forward
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