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If Q: R" → R is a quadratic form, explain how to determine the maximum and minimum values that Q takes on the set of all vectors x € R" such that x 1, and to find a vector of norm I on which the maximum and minimum values are attained. (3) Illustrate this procedure in the case where Q: R →R is of the form Q12 +2r2+ Is 2r ++2rs+.

If Q: R" → R is a quadratic form, explain how to determine the maximum and minimum values that Q takes on the set of all vectors x € R" such that x 1, and to find a vector of norm I on which the maximum and minimum values are attained. (3) Illustrate this procedure in the case where Q: R →R is of the form Q12 +2r2+ Is 2r ++2rs+.

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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(a) If Q: R" -R is a quadratie form, explain how to determine the maximum and minimum values that Q takes on the set of all vectors x R" such that x = 1, and to find a vector of norm 1 on which the maximum and minimum values are attained. (b) Illustrate this procedure in the case where Q R'R is of the form Q2 f+2r2+ 2r + + 2rzs +.
Transcribed Image Text:(a) If Q: R" -R is a quadratie form, explain how to determine the maximum and minimum values that Q takes on the set of all vectors x R" such that x = 1, and to find a vector of norm 1 on which the maximum and minimum values are attained. (b) Illustrate this procedure in the case where Q R'R is of the form Q2 f+2r2+ 2r + + 2rzs +.
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