Consider the following matrix:-60 0-4A =0 04-12 18 -2 027 -18 0 3a) Find the distinct eigenvalues of A, their multiplicities, and the dimensions of their associated eigenspaces.Number of Distinct Eigenvalues: 1Eigenvalue: 0 has multiplicity 1 and eigenspace dimension 1b) Determine whether the matrix A is diagonalizable.Conclusion: < Select an answer >< Select an answer >Official Time:4 is diagonalizableA is not diagonalizable

Answered: Image /qna-images/answer/057b451a-7076-4c45-9d9a-6b538d5706d3.jpg

Answered: Consider the following matrix: -6 0 0…

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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. Find all eigenvalues of the matrix vector for each eigenvalue. -16 8 -40 20 and an (explicit) eigen- . Verify that the Cayley-Hamilton Theorem holds for the matrix A = -16 8 -40 20
Consider the following matrix: 1 -6 -6 -6 -4 -2 -2 8 -6 0 0 12 -1 -3 -3 0 A = a) Find the distinct eigenvalues of A, their multiplicities, and the corresponding number of basic eigenvectors. Number of Distinct Eigenvalues: 1 Eigenvalue: 0 has multiplicity 1 and corresponding number of basic eigenvectors 1 b) Determine whether the matrix A is diagonalizable. Conclusion: Official Time: A is diagonalizable A is not diagonalizable SUBMIT AND MARK
Consider the following matrix: A = ..comm 3 0 0 00 03 0 -5 0-12 -3 12 000-2 a) Find the distinct eigenvalues of A, their multiplicities, and the corresponding number of basic eigenvectors. Number of Distinct Eigenvalues: 1 Eigenvalue: 0 has multiplicity 1 and corresponding number of basic eigenvectors 1 b) Determine whether the matrix A is diagonalizable. Conclusion: A is diagonalizable Question 13 A is diagonalizable A is not diagonalizable sk dom A in the diagonalizablo matrix boloy and P-1AP-D for
Consider the following matrix: A = 1 0-3 -9 -9 -2 2 -6 -18 -18 002 0 0 00 -3 -8 -9 003 10 11 a) Find the distinct eigenvalues of A, their multiplicities, and the dimensions of their associated eigenspaces. Number of Distinct Eigenvalues: 1 Eigenvalue: 0 has multiplicity 1 and eigenspace dimension 1 b) Determine whether the matrix A is diagonalizable. Conclusion: A is diagonalizable A is not diagonalizable SUBMIT AND MARK SAVE AN
A = [2 -1 |-2 3] let it be. a) Write the characteristic polynomial of the matrix A b)Find the eigenvalues and eigenspaces corresponding to this matrix. c) Is matrix A diagonalizable? Show me. d) A^8 =? (Guidance: Do not apply matrix multiplication. D = (P^-1)AP make use of)
A = 1 1 -1 vi) Determine the matrix V and the matrix vii Check that A = UEVT. L Find a SVD for A by following the steps: i) Compute the matrix M = ATA ii) Find the characteristic polynomial, eigenvalues, and their algebraic multiplicities for M iii) Find the singular values for A iv) Determine an orthonormal eigenbasis for each eigenvalue of M v) Write down the matrix U. Remember U must be orthogonal.
3. Let x ER", A, B E Rnxn and || || be some vector norm (same notation is used for the corresponding operator norm). Show that || Ax|| ≤ ||A||||||, ||AB|| ≤ ||A|||| B|| and ||I|| = 1. Show by counterexample that ||- ||max and ||- ||F are not operator norms. ||AB|| 2 Hint: Find matrices A, B € R²×2 such that some of the properties in (1) do not hold. Note that ||I|| max = 1. In addition, the Frobenius norm satisfies the second inequality in (1): let AT = [a₁,..., an] and B = [b₁, ...,b], so that n n n n ·Σ (a{b;)² ≤ Σ ||a₁||²||6,;||³² = Σ || a;||²Σ||6; ij=1 i,j=1 i=1 j=1 n n = Σ |aki|² Σ |b₁j|² = || A||²|| B||²| i,k=1 j,l=1 (1) where the Cauchy-Schwarz inequality was used. 1/2
A company who makes flotation devices has products that come in many different shapes and sizes. Complete parts a and b below using the figures shown to the right. Use the a button on your calculator. Base part (a) Base part (b) a) Determine the volume, in cubic inches, of a flotation device that is in the shape of a 4.5-ft-long solid octagonal prism whose base has an area of 4 in.2.
b) Find (if possible) a nonsingular matrix P such that P AP is diagonal. Verify that P is a diagonal matrix with the eigenvalues on the main diagonal, where 3 2 -3] A=-3 -4 -1 -2 9.
For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 1 2 4 1 2 P = A = I P-¹AP = N|H m/~ 3 -1 Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal.
Find the eigenvalues of the matrix -3 3 -3 -6 6 -3 -9 9 For each eigenvalue, find an eigenvector or some eigenvectors that form a basis for the corre- sponding eigenspace.

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