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(a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x*, y") for the constrained optimisation problem were (-0.47,0.88) and (0.47,0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.

(a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x*, y") for the constrained optimisation problem were (-0.47,0.88) and (0.47,0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.

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 2 Consider the bordered Hessian matrix obtained from the constrained optimisation problem and answer the following questions about the matrix: 2x 2y 0 2x 12x² 0 2y 0 2 (a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x*,y*) for the constrained optimisation problem were (-0.47,0.88) and (0.47, 0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.
Transcribed Image Text:Question 2 Consider the bordered Hessian matrix obtained from the constrained optimisation problem and answer the following questions about the matrix: 2x 2y 0 2x 12x² 0 2y 0 2 (a) For which range of values of x and y would the matrix be positive definite? (b) For which range of values of x and y would the matrix be negative definite? (c) You are now told that the critical points (x*,y*) for the constrained optimisation problem were (-0.47,0.88) and (0.47, 0.88) respectively. Taking into consideration your answers in part (a) and (b) above, would you conclude that each of the critical points are a maximum, a minimum, or a saddle point? Explain.
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