8.M.2 One can define a bilinear form on R2 by the formula ‹ [ 8 ], [ 8 ]› = ac − 3ad − 3bc + 7bd. a) What is the Gram matrix G of this bilinear form (with respect to the standard basis)? b) Find the eigenvalues of G. c) Is the bilinear form positive definite? If not, find a vector v such that (v, v) ≤ 0.
8.M.2 One can define a bilinear form on R2 by the formula ‹ [ 8 ], [ 8 ]› = ac − 3ad − 3bc + 7bd. a) What is the Gram matrix G of this bilinear form (with respect to the standard basis)? b) Find the eigenvalues of G. c) Is the bilinear form positive definite? If not, find a vector v such that (v, v) ≤ 0.
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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![8.M.2 One can define a bilinear form on R² by the formula
a
(8] [8]
|) = ac - 3ad - 3bc + 7bd.
a) What is the Gram matrix G of this bilinear form (with respect to the standard basis)?
b) Find the eigenvalues of G.
c) Is the bilinear form positive definite? If not, find a vector v such that (u, v) ≤ 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc86af83d-c04b-4d1f-8f1b-1d87f63f73a5%2F1879660b-c508-4b6b-a3d9-ebb285816dd3%2Fs42ybwt_processed.png&w=3840&q=75)
Transcribed Image Text:8.M.2 One can define a bilinear form on R² by the formula
a
(8] [8]
|) = ac - 3ad - 3bc + 7bd.
a) What is the Gram matrix G of this bilinear form (with respect to the standard basis)?
b) Find the eigenvalues of G.
c) Is the bilinear form positive definite? If not, find a vector v such that (u, v) ≤ 0.
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