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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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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.
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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