0 -21314.31 = 2, 3 Diagonalize the matrices in Exercises 7-20, if possible. The rouleigenvalues for Exercises 11-16 and 18 are included below thematrix.

Given that 20-2132003 is a 3×3 matrix.

Answered: Diagonalize the matrices in Exercises…

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.
Let A E BL(H). Then A is called normal if A*A = AA*, uni- tary if A*A = I = AA*, that is, A* = A-¹, and self-adjoint if A* = A. Clearly, if A is unitary or self-adjoint, then A is normal. How- ever, a normal operator need be neither unitary nor self-adjoint. For example, let H = K² and for x = (x(1), x(2)) in H, A(x) = (x(1) − x(2), x(1) + x(2)). Then it can be easily seen that for x = H, A*(x) = (x(1) + x(2), −x(1) + x(2)), Request A*A(z) = 2(x(1),z(2)) = AA*(x). Hence A*A = AA*, but A*A# I and A* ‡ A. explain these steps in détail.
Please answer it within 30 minutes.I will upvote! Which one of the above statement is correct.Explain the correct statements inin detail.
Determine whether the standard matrix is a projection, reflection, a rotation, or none of these.
Find a 2 x 2 matrix A such that the entries of A are all real numbers and –4 is an eigenvalue of A, or explain why no such matrix exists.
Diagonalize the matrices in Exercises 7-20, if possible. The roul eigenvalues for Exercises 11-16 and 18 are included below the matrix.
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)
(Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) Also when writing the answer, write it in the way that the computer/WebAssign wants thank you!

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Diagonalize the matrices in Exercises 7-20, if possible. The real eigenvalues for Exercises 11–16 and 18 are included below the matrix