# 3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each... 3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each eigenspace and state whether the matrix is diagonalizable or not. 1 6 -40 -7 0 0 -3 oni

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• ### 3 3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of... 3 3. (10 points) Determine the multiplicity of each eigenvalue and a basis and dimension of each eigenspace and state whether the matrix is diagonalizable or not. 6 -7 -3 1 4 -4 0 0 0

• ### Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2... Find a basis for each eigenspace and calculate the geometric multiplicity of each eigenvalue. 3 2 The matrix A = 0 2 0 has eigenvalues X1 = 2 and X2 1 2 3 For each eigenvalue di, use the rank-nullity theorem to calculate the geometric multiplicity dim(Ex). Find the eigenvalues of A = 0 0 -1 0 0 geometric multiplicity of each eigenvalue. -7- Calculate the algebraic and

• ### It can be shown that the algebraic multiplicity of an eigenvalue is always greater than or... It can be shown that the algebraic multiplicity of an eigenvalue is always greater than or equal to the dimension of the eigenspace corresponding to 2. Find h in the matrix A below such that the eigenspace for 1 = 8 is two-dimensional. 8 -2 4-4 6 h 0 A. оооо 5 08 00 2 The value of h for which the eigenspace for 1 = 8 is two-dimensional ish- We were unable to transcribe this image

• ### Corresponding eigenvectors of each eigenvalue 9 Let 2. (as find the eigenvalues of A GA 1... Corresponding eigenvectors of each eigenvalue 9 Let 2. (as find the eigenvalues of A GA 1 -- 1 and find the or A each 5 Find the corresponding eigenspace to each eigen value of A. Moreover, Find a basis for The Corresponding eigenspace (c) Determine whether A is diagonalizable. If it is, Find a diagonal matrix ) and an invertible matrix P such that p-AP=1

• ### -8 -24 -12 (16 points) Let A= 0 4 0 6 12 10 (a) (4 points)... -8 -24 -12 (16 points) Let A= 0 4 0 6 12 10 (a) (4 points) Find the eigenvalues of A. (b) [6 points) For each eigenvalue of A, find a basis for the eigenspace of (b) [6 points) is the matrix A diagonalizable? If so, find matrices D and P such that is a diagonal matrix and A = PDP 1. If not, explain carefully why not.

• ### 1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5... 1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...

• ### Commenting no idea is not helpful and doesn't mean my question needs to be edited. The... Commenting no idea is not helpful and doesn't mean my question needs to be edited. The answer is A and C are false, I'd like a good explanation. Review 4: question 2 Let A be an n x n matrix. Which of the below is/are not true? A Matrix A is diagonalizable if and only if the dimension of each eigenspace is less than the multiplicity of the corresponding eigenvalue. B Matrix A is diagonalizable if and only if it...

• ### Question 1: Question 2: Thx, will give a thumb Determine the algebraic and geometric multiplicity of... Question 1: Question 2: Thx, will give a thumb Determine the algebraic and geometric multiplicity of each eigenvalue of the matrix. 2 3 3 3 2 3 3 3 2 Identify the eigenvalue(s). Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is one distinct eigenvalue, 1 = OB. There are two distinct eigenvalues, hy and 12 (Use ascending order.) OC. There are three distinct eigenvalues, 14 , 22 = (Use...

• ### 3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4 3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4 3 0 2 0 The matrix A=11 3 1 0 10 has eigenvalue t. Find a basis for the eigenspace E9) 0 0 0 4

• ### 7. (14 points) Let A = An eigenvalue of A is = 3. Find a basis... 7. (14 points) Let A = An eigenvalue of A is = 3. Find a basis for the eigenspace of A corresponding to 1 = 3. - 

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