Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Chapter 5.5, Problem 4EQ
To determine
To find: The quadratic form of
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In Exercise, evaluate the quadratic form f(x) = xTAx for the given A andx.
Let
A =
and define a quadratic form by Q(v) = v Av. Then
Q(x, y, z) =
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Find an orthogonal change of variables, x = Py, that transforms the quadratic form
q(x) = x² + x²+2x1x2 − 2x2x3
into a quadratic form no cross-product form. Write the new quadratic form.
Chapter 5 Solutions
Linear Algebra: A Modern Introduction
Ch. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - Prob. 2EQCh. 5.1 - Prob. 3EQCh. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - In Exercises 1-6, determine which sets of vectors...Ch. 5.1 - Prob. 6EQCh. 5.1 - Prob. 7EQCh. 5.1 - Prob. 8EQCh. 5.1 - In Exercises 7-10, show that the given vectors...Ch. 5.1 - In Exercises 7-10, show that the given vectors...
Ch. 5.1 - Prob. 11EQCh. 5.1 - In Exercises 11-15, determine whether the given...Ch. 5.1 - In Exercises 11-15, determine whether the given...Ch. 5.1 - Prob. 14EQCh. 5.1 - Prob. 15EQCh. 5.1 - In Exercises 29-32, use Exercise 28 to determine...Ch. 5.1 - In Exercises 29-32, use Exercise 28 to determine...Ch. 5.2 - Prob. 15EQCh. 5.2 - In Exercises 15-18, find the orthogonal projection...Ch. 5.2 - Prob. 17EQCh. 5.2 - Prob. 18EQCh. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.2 - In Exercises 19-22, find the orthogonal...Ch. 5.5 - In Exercises 1-6, evaluate the quadratic form for...Ch. 5.5 - Prob. 2EQCh. 5.5 - Prob. 3EQCh. 5.5 - Prob. 4EQCh. 5.5 - Prob. 5EQCh. 5.5 - Prob. 6EQCh. 5.5 - Prob. 7EQCh. 5.5 - Prob. 8EQCh. 5.5 - Prob. 9EQCh. 5.5 - Prob. 10EQCh. 5.5 - In Exercises 7-12, find the symmetric matrix A...Ch. 5.5 - Prob. 12EQCh. 5.5 - Prob. 19EQCh. 5.5 - Classify each of the quadratic forms in Exercises...Ch. 5.5 - Prob. 21EQCh. 5.5 - Prob. 22EQCh. 5.5 - Prob. 23EQ
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- Write the quadratic function in the standard form y = a(x - h)² + k. y = x² - 6x y = (x + 6)²-6 Oy = (x+3)²-3 Oy=(x-6)²-36 Oy=(x-3)²-9arrow_forward1. Put the following quadratic functions into factored form, y = a(x –r)(x – s), and state the x intercepts. a. y = x² + 2x – 15 Factored form y = x interceptsarrow_forwardFind expressions for the quadratic functions whose graphs are shown. f(x) = || g(x) = y X X (-2,2) va y 7 (0, 1) (8, 2) (1, -2.5) X Xarrow_forward
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