3. Let A = 2 -3 -4O- 23Owomano1i. Find the characteristic polynomial and use it to computethe eigenvalues of A.ii. Determine whether A is diagonalizable. If it is then findon invertible matrix P and a diagonal matrix D Suchthat A=POP, If it is not, then explain why not.ii. Is A orthogonally diagonalizable? Yes or No?

Answered: Image /qna-images/answer/627242a0-9a71-4a29-965b-0cc7e7834964.jpg

Answered: 3. Let A = 2 -3 -4 O -2 3 O 1 i. Find…

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.
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. If two matrices A and B have the same characteristic polynomial,then Aand B musthaveexactlythesame set of eigenvalues.
Let A be an 3 by 3 matrix. Select all true statements below. A. If A is diagonalizable, then A has 3 distinct real eigenvalues. B. If A has 3 linearly independent eigenvectors, then A is diagonalizable. C. The matrix A may or may not be diagonalizable. D. The matrix A is certainly diagonalizable. E. If A has 3 distinct real eigenvalues, then A is diagonalizable. OF. If A is diagonalizable, then A has 3 linearly independent eigenvectors. G. None of the above
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2. Find the characteristic polynomial, eigenvalues, eigenvectors, and (if possible) an invertible matrix P such that P-¹BP is diagonal where B = 1 2 1 -2 3 6 -6 2
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. The statement is false. The multiplicity of a root r of the characteristic equation of A is the number of eigenvectors corresponding to that root. The statement is true. It is the definition of the multiplicity of a root of the characteristic equation of A. The statement is true. It is the definition of the algebraic multiplicity of an eigenvalue of A. OThe statement is false. The multiplicity of a rootr of the characteristic equation. of A is called the geometric multiplicity of r as an eigenvalue of A.
Create a 3 × 3 matrix A from the 9 numbers you randomly generated. 00 86 8 75 99 22 61 72 67 2. Compute the characteristic polynomial. Is λ = 0 an eigenvalue? 3. From the equivalent statements theorem, what can you say about each of the following? A. Solutions of the system of equations Ax = 0 B. Solutions of the system of equations Ax →> C. The span of the column vectors of A D. The orthogonal complement of the null space of A E. The invertibility of the matrix A. -

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