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Consider an n x n matrix M that is not symmetric, and define the function g(x) = x Mx

Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher ISBN: 9780136009269 434

Solution for problem 23 Chapter 8.2

Linear Algebra with Applications | 4th Edition

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Linear Algebra with Applications | 4th Edition | ISBN: 9780136009269 | Authors: Otto Bretscher

Linear Algebra with Applications | 4th Edition

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Problem 23

Consider an n x n matrix M that is not symmetric, and define the function g(x) = x Mx from Rn to R. Is g necessarily a quadratic form? If so, find the matrix of g.

Step-by-Step Solution:
Step 1 of 3

M303 Section 1.8 Notes- Introduction to Linear Maps/Transformations 9-19-16  If is × matrix, then for any vector ℝ , multiplication by produces new vector ℝ ; if we regard vectors in ℝ as inputs on which acts by multiplication to give output in ℝ , and we arrive at notion of a function  Function/map :ℝ → ℝ - rule which assigns unique output ℝ to each input ℝ goes from domain ℝ to target ℝ o Image of under - output

Step 2 of 3

Chapter 8.2, Problem 23 is Solved
Step 3 of 3

Textbook: Linear Algebra with Applications
Edition: 4
Author: Otto Bretscher
ISBN: 9780136009269

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Consider an n x n matrix M that is not symmetric, and define the function g(x) = x Mx