1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to x"Ax), (ii) find matrices P, orthonormal, and D so that D diagonal, (iii) write the quadratic form in terms of y1,..., Yn where x = decide whether the form is positive/negative definite/semidefinite or indefinite. (a) 2x – 2x1x2 + 2x3 (b) –xỉ + 4x1x2 – 4x3 (c) 3x? + 4.x3 + 5xž + 4x1x2 – 4x2X3 (it may help to show that A characteristic polynomial of A). РТ АР is Py and (iv) 1 is a root of the %3D
1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to x"Ax), (ii) find matrices P, orthonormal, and D so that D diagonal, (iii) write the quadratic form in terms of y1,..., Yn where x = decide whether the form is positive/negative definite/semidefinite or indefinite. (a) 2x – 2x1x2 + 2x3 (b) –xỉ + 4x1x2 – 4x3 (c) 3x? + 4.x3 + 5xž + 4x1x2 – 4x2X3 (it may help to show that A characteristic polynomial of A). РТ АР is Py and (iv) 1 is a root of the %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 29E
Related questions
Question
B please
![1. For the following quadratic forms (i) write down the symmetric matrix A (so the form
is equal to x"Ax), (ii) find matrices P, orthonormal, and D so that D = PT AP is
diagonal, (iii) write the quadratic form in terms of y1,..., Yn where x = Py and (iv)
decide whether the form is positive/negative definite/semidefinite or indefinite.
(a) 2x – 2x1x2 + 2x3
(b) —г? + 4122 — 4л2
(c) 3xỉ + 4x3 + 5x3 + 4x1x2 – 4x2x3 (it may help to show that A = 1 is a root of the
characteristic polynomial of A).
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb21c0740-4bbb-4c6d-b879-fe474f9c69f2%2Fb7bc7a30-470b-4b21-9fea-8ac99686a4f7%2F0m0slnq_processed.png&w=3840&q=75)
Transcribed Image Text:1. For the following quadratic forms (i) write down the symmetric matrix A (so the form
is equal to x"Ax), (ii) find matrices P, orthonormal, and D so that D = PT AP is
diagonal, (iii) write the quadratic form in terms of y1,..., Yn where x = Py and (iv)
decide whether the form is positive/negative definite/semidefinite or indefinite.
(a) 2x – 2x1x2 + 2x3
(b) —г? + 4122 — 4л2
(c) 3xỉ + 4x3 + 5x3 + 4x1x2 – 4x2x3 (it may help to show that A = 1 is a root of the
characteristic polynomial of A).
-
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning