A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below.Q(Py) = 11y1 + 6y²2If the eigenvectors of the original matrix are as follows:[1]2Find the matrices P and D such that A = PDPTV₁ =D=P=V2 =

Answered: Image /qna-images/answer/469f3e4b-7bb0-4870-97e6-4f4b67f9813e.jpg

A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below. Q(Py) = 11y + 6y/2 If the eigenvectors of the original matrix are as follows: V1 = D= 1₁ Find the matrices P and D such that A P= v2 = = PDPT

A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below. Q(Py) = 11y + 6y/2 If the eigenvectors of the original matrix are as follows: V1 = D= 1₁ Find the matrices P and D such that A P= v2 = = PDPT

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

Q: Consider a matrix A = a C where a, b, c are real numbers such that abc = 1 and a² + b² + c? = 3. (a)…

Q: find the eigen values and Of the matrix eigen vectors 2

Q: For each matrix; find its characteristic polynomial, its eigenvalues/spaces, and its algebraic and…

Q: 0031 0003 -1 600 -2600 (b) B = 0 030 0 003

Q: Suppose the matrix, A, has eigenvectors 00-0 respectively. Use this order of eigenvectors to find…

A: It is provided that the eigenvectors of A are 101, 011, 201 and the corresponding eigenvalues are…

Q: A = -53 -70 35 45

Q: . Let A = -3 the matrix A. 93). Is it true that A is orthogonally diagonalizable? If yes,…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: For a matrix M, Mv = \v, evaluate = (Mv)iv in two different ways to find a condition on the…

A: Follow step 2nd.

Q: natrix. Suppose )₁ are given vect the eigen values

Q: Diagonalize each matrix, if possible. Find the eigenvalues, if none are given, and state the…

A: By Bartleby policy I have to solve only first one as these are unrelated & very lengthy…

Q: Find the matrix A of the quadratic form associated with the equation. Then find the eigenvalues of A…

A: The given quadratic form is 3x2-23xy+y2+2x+23y=0. We have to find the matrix A associated with the…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that PAP is diagonal. (If not…

Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: The 3 x 3 matrix A has eigenvalues a, 2 and 2a. Find the values of a, ß and 0 for which 4A-¹ = A² +…

Q: 4. Suppose f: [a, b] → R is continuous. Let g = inff. Show that there is a point ro in [a, b] such…

A: This is the question of Real analysis and topology.

Q: Suppose matrix A as follows: 2 -17 3 -2 0 ^ = [2 -1 a. Find the eigenvalues and eigenvectors of the…

Q: Suppose A is a 2 × 2 matrix. Use the characteristic equation to show that A and A¹ have the same…

A: We have to show that have same eigenvalues using given data.Concept required:Eigenvalues of are…

Q: Find a 2 x 2 matrix such that [3]==1] (incorrect) 4 -2 -2 Answer(s) submitted: C

Q: Let C be a 6x6 matrix with. real eigenvalues -1, 2,4 and no complexores. Write the characterstic…

Q: Find the matrix A of the quadratic form assoe 2x2 - 3xy - 2y2 + 11 = 0 A = Find the eigenvalues of…

Q: Find the matrix A of the quadratic form associated with the equation. 6x2 - 5xy - 6y2 + 12 = 0 A =…

Q: For the matrix, list the real eigenvalues, repeated according to their multiplicities. 3 -20 4 0 21…

A: if the given matrix is A then eigen value are:- det(A-lembda i)=0

Q: For the matrix, list the real eigenvalues, repeated according to their multiplicities. The real…

Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

A: Our objective is given below:

Question

A change of variable, x = Py, is made to transform the original quadratic form into one with no cross product. The new quadratic form is given below.
Q(Py) = 11y1 + 6y²2
If the eigenvectors of the original matrix are as follows:
[1]
2
Find the matrices P and D such that A = PDPT
V₁ =
D=
P=
V2 =

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Determine the eigen value

VIEW

Step 2: Determine the matrix P & D

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

P =

0	1
1	0

and D =

6	0
0	11

do not seem to be the correct answers, may there be a mistake somewhere? I went through by myself and got a similar answer, but it was also deemed incorrect. Just a bit confused.

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are -2 and 7. 3 - 4 - 2 -4 3 - 2 -2 -2 6 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are - 10, 2, and - 2. - 4 - 4 - 2 A = - 4 -2 - 4 2 -4 - 4 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 11 and 2. 6 4-2 4 6 -2 -2 -2 3 Enter the matrices P and D below. (Use a comma to separate matrices as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
i) By using the inverse of the coefficients matrix [A] belonging to the set of equations given above, using the [L][U] method. find it. Check the result with [A][A]^-1 = [I].ii) Find the unknown vector {X} of the above system of equations by using the found [A]^-1 matrix.{X}=[A]^-1[B]iii) Solve the system of equations using the [L][U] method and find the results in (ii) Compare with. Find the determinant of the coefficients matrix.
Q6: Solve for matrix X in the matrix equation X – A" = 21, where I is a unit matrix with size 2 × 2 and A =
Express the quadratic form T as v Av, where A is a symmetric matrix. x² + 3y² + 5z² − 4xy+3yz + 10xz
FULLY SOLVE AND MAKE ANSWERS CLEAR TO READD!
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 10 and -9. A = 1 -3 9 -3 93 9 3 1 Enter the matrices P and D below. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed. Do not label the matrices.)
Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) λ; = 07 77 For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x) = 6 Need Help? Read It X
please,don't provide handwriting solution...