Question

True/False? If 0 is an eigenvalue of a 3x3 matrix A with geometric multiplicity ug(A,0)=3, then...

True/False? If 0 is an eigenvalue of a 3x3 matrix A with geometric multiplicity ug(A,0)=3, then A is the zero-matrix, that is A=0

The answer is True, but I don't understand why.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The matrix A has an eigenvalue λ with an algebraic multiplicity of 5 and a geometric...
The matrix A has an eigenvalue λ with an algebraic multiplicity of 5 and a geometric multiplicity of 2. Does A have a generalised eigenvector of rank 3 corresponding to λ? What about a generalised eigenvector of rank 5?
Let A be a matrix with an eigenvalue λ that has an algebraic multiplicity of k,...
Let A be a matrix with an eigenvalue λ that has an algebraic multiplicity of k, but a geometric multiplicity of p < k, i.e. there are p linearly independent generalised eigenvectors of rank 1 associated with the eigenvalue λ, equivalently, the eigenspace of λ has a dimension of p. Show that the generalised eigenspace of rank 2 has at most dimension 2p.
The matrix A= 1 0 0 -1 0 0 1 1 1 3x3 matrix has two...
The matrix A= 1 0 0 -1 0 0 1 1 1 3x3 matrix has two real eigenvalues, one of multiplicity 11 and one of multiplicity 22. Find the eigenvalues and a basis of each eigenspace. λ1 =..........? has multiplicity 1, with a basis of .............? λ2 =..........? has multiplicity 2, with a basis of .............? Find two eigenvalues and basis.
Explain the distinction between algebraic multiplicity and geometric multiplicity of a matrix. Justify your answer (explain)...
Explain the distinction between algebraic multiplicity and geometric multiplicity of a matrix. Justify your answer (explain) These questions follow the exercises in Chapter 4 of the book, Scientic Computing: An Introduction, by Michael Heath. They study some of the properties of eigenvalues, eigenvectors, and some ways to compute them.
2. ?̇=??, ?= [3 −18 ; 2 −9]. (1) Find the eigenvalue of multiplicity two and...
2. ?̇=??, ?= [3 −18 ; 2 −9]. (1) Find the eigenvalue of multiplicity two and their corresponding (generalized) eigenvectors ?1= [3;?] and ?2= [?;0] respectively. (2) Let ?= ?^−1??.Find the matrix B. (3) Find ???. (4) Find the general solution of ?̇ = ??. (5) Let ?=??.Find the general solution of ?̇ = ??. (6) Find the solution with initial values x(0) =[4; 1].
2.  For each 3*3 matrix and each eigenvalue below construct a basis for the eigenspace Eλ. A=...
2.  For each 3*3 matrix and each eigenvalue below construct a basis for the eigenspace Eλ. A= (9 42 -30 -4 -25 20 -4 -28 23),λ = 1,3 A= (2 -27 18 0 -7 6 0 -9 8) , λ = −1,2 3. Construct a 2×2 matrix with eigenvectors(4 3) and (−3 −2) with eigen-values 2 and −3, respectively. 4. Let A be the 6*6 diagonal matrix below. For each eigenvalue, compute the multiplicity of λ as a root of the...
Which of the following are NECESSARY CONDITIONS for an n x n matrix A to be...
Which of the following are NECESSARY CONDITIONS for an n x n matrix A to be diagonalizable? i) A has n distinct eigenvalues ii) A has n linearly independent eigenvectors iii) The algebraic multiplicity of each eigenvalue equals its geometric multiplicity iv) A is invertible v) The columns of A are linearly independent NOTE: The answer is more than 1 option.
(6) Label each of the following statements as True or False. Provide justification for your response....
(6) Label each of the following statements as True or False. Provide justification for your response. (b) True/False The scalar λ is an eigenvalue of a square matrix A if and only if the equation (A − λIn)x = 0 has a nontrivial solution. (c) True/False If λ is an eigenvalue of a matrix A, then there is only one nonzero vector v with Av = λv. (d) True/False The eigenspace of an eigenvalue of an n × n matrix...
205 Tl is expected to be stable. True or False? the answer is true, but I...
205 Tl is expected to be stable. True or False? the answer is true, but I don't understand why if the ratio of N/Z is 124/81?
Decide if each of the following statements are true or false. If a statement is true,...
Decide if each of the following statements are true or false. If a statement is true, explain why it is true. If the statement is false, give an example showing that it is false. (a) Let A be an n x n matrix. One root of its characteristic polynomial is 4. The dimension of the eigenspace corresponding to the eigenvalue 4 is at least 1. (b) Let A be an n x n matrix. A is not invertible if and...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT