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Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a)...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1...
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in...
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3
[0 1 1 1 0 1 1 1 1 0 1 1. Let A and b...
[0 1 1 1 0 1 1 1 1 0 1 1. Let A and b 1 1 1 0 Find the eigenvalues of A. Find four independent eigenvectors of A. Ar for each eigenvector T. Verify that Ar Find the coordinates of b in the eigenbasis. . Find the matrix of A relative to the eigenbasis. Find a matrix P such that PAP is diagonal. Find four ort hogonal eigenvectors of A Find the coordinates of b in the...
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
Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positiv...
Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...
Please help and explain all steps 9 Marks [5 0 0 1 8. Let A= 10...
Please help and explain all steps
9 Marks [5 0 0 1 8. Let A= 10 3 [0 0 -2] (a) Find all eigenvalues of A and their corresponding eigenvectors. (b) Is A diagonalizable? If so, find a matrix P and diagonal matrix D such that P-1AP = D.
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each e...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
Question 4 11 pts Each blank is 1 point) 0 Let A - 0 0 3...
Question 4 11 pts Each blank is 1 point) 0 Let A - 0 0 3 (al. Find (A) where A, means A, with = 2 (b). For what value of x is A, + I not invertible? or (Please fill it in from small to large for this two blank). Please write the answer to the following problems and upload the answer in one pdf ble after you finish and submit this final (12 points) Lett be a linear...
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6...
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
1 1 -21 2. Problem 2 Let A= -1 2 1 0 1 -1/ (a) (1 point) Find the eigenvalues and eigenvectors of A. Solution: vastam 2 101 - 60: (b) (1 point) Find the eigenvectors of A. Solution: (c) (1 point) Find an invertible matrix P such that P-AP = D, where D is a diagonal matrix. Solution:
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3
Find the Eigenvalues, Eigenvectors, If possible find an invertible matrix P, such that P-AP is in diagonalized form. -3 1 A = 4 3 () 0 0 -2 A = 1 2 1 0 3
[0 1 1 1 0 1 1 1 1 0 1 1. Let A and b 1 1 1 0 Find the eigenvalues of A. Find four independent eigenvectors of A. Ar for each eigenvector T. Verify that Ar Find the coordinates of b in the eigenbasis. . Find the matrix of A relative to the eigenbasis. Find a matrix P such that PAP is diagonal. Find four ort hogonal eigenvectors of A Find the coordinates of b in the...
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
Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...
Please help and explain all steps
9 Marks [5 0 0 1 8. Let A= 10 3 [0 0 -2] (a) Find all eigenvalues of A and their corresponding eigenvectors. (b) Is A diagonalizable? If so, find a matrix P and diagonal matrix D such that P-1AP = D.
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
Question 4 11 pts Each blank is 1 point) 0 Let A - 0 0 3 (al. Find (A) where A, means A, with = 2 (b). For what value of x is A, + I not invertible? or (Please fill it in from small to large for this two blank). Please write the answer to the following problems and upload the answer in one pdf ble after you finish and submit this final (12 points) Lett be a linear...
) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal...
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