Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.2 1 1A = 1 2 11121 24002= 2 0-2 0 102-1 0 001- 16- 16 -|m-182/31 11ح اس3 31661 13-6Select the correct choice below and fill in the answer boxes to complete your choice.(Use a comma to separate vectors as needed.)O A. There is one distinct eigenvalue, λ = . A basis for the corresponding eigenspace is {}.=O B. In ascending order, the two distinct eigenvalues are ₁ and 2₂ =OC. In ascending order, the three distinct eigenvalues are ₁ = ₂ = ₁ and 23 = |22Bases for the corresponding eigenspaces are {and {}, respectively.Bases for the corresponding eigenspaces are {}, {}, and {}, respectively.

Answered: Matrix A is factored in the form PDP-1.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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decide if the given statement is true or false,and give a brief justiﬁcation for your answer. If true, you can quote a relevant deﬁnition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false. Q. The eigenvalues of an upper or lower-triangular matrix A are the entries appearing on the main diagonal of A.
Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 0 9 9 9 0 9 9 9 9 d; = For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x;) =
Find a basis for the eigenspace corresponding to the eigenvalue. 4 - 3 3 A = 6 , 1 = 3 - 2 -6 -3 A basis for the eigenspace corresponding to 1 = 3 is { }. (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Use a comma to separate answers as needed.)
Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save time, the eigenvalues are 11 and -7 18 4 81 4 -5 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) 4
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Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 044 404 444 For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x) -
Let -1 -8 A = 1 0 0 1 Find the eigenvalues, and bases for the eigenspaces.
Matrix A is factored in the form PDP¯1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 20 - 16 – 40 - 1 6 0 0 0 0 1 A= 8 6 32 1 060 2 1 8 0 0 6 1 0 0 0 0 2 -10 - 4 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) O A. There is one distinct eigenvalue, À = A basis for the corresponding eigenspace is { }. O B. In ascending order, the two distinct eigenvalues are = and 2 = Bases for the corresponding eigenspaces are { } and {}, respectively. O C. In ascending order, the three distinct eigenvalues are , = 12 = Bases for the corresponding eigenspaces are {}. { }, and {}, respectively. and A3 = Click to select and enter your answer(s). DELL
Find the matrix A of the quadratic form associated with the equation. 4x² - 6xy - 4y² + 6 = 0 A = 4 -3 P = -3 -4 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) λ = 5, -5 Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) [1,0], [0,1]
Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated list.) 50 1 0 1 2 0 0 2
Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter your answers from smallest to largest.) 033 0 3 3 3 3 λ; = For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.) dim(x;) =

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