Homework Answers
Let M = [P|I4] =
|
1 |
-1 |
0 |
1 |
1 |
0 |
0 |
0 |
|
1 |
-1 |
0 |
-1 |
0 |
1 |
0 |
0 |
|
1 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
|
1 |
1 |
-1 |
0 |
0 |
0 |
0 |
1 |
The RREF of M is
|
1 |
0 |
0 |
0 |
1/4 |
1/4 |
1/4 |
1/4 |
|
0 |
1 |
0 |
0 |
-1/4 |
-1/4 |
1/4 |
1/4 |
|
0 |
0 |
1 |
0 |
0 |
0 |
1/2 |
-1/2 |
|
0 |
0 |
0 |
1 |
1/2 |
-1/2 |
0 |
0 |
This implies that P-1 =
|
1/4 |
1/4 |
1/4 |
1/4 |
|
-1/4 |
-1/4 |
1/4 |
1/4 |
|
0 |
0 |
1/2 |
-1/2 |
|
1/2 |
-1/2 |
0 |
0 |
On multiplication, P-1 AP = D (say) =
|
1 |
0 |
0 |
0 |
|
0 |
0.6 |
0 |
0 |
|
0 |
0 |
0.7 |
0 |
|
0 |
0 |
0 |
0.7 |
Since P-1 AP = D is a diagonal matrix, hence A is diagonalalizab
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Consider the following. 0.75 0.05 0.10 0.10 0.05 0.75 0.10 0.10 A= 0.10 0.10 0.75 0.05...
Consider the following. 1 -1 0 1 A= 1 -1 0-1 0.80 -0.10 0.15 0.15 -0.10...
Consider the following. 1 -1 0 1 A= 1 -1 0-1 0.80 -0.10 0.15 0.15 -0.10 0.80 0.15 0.15 0.15 0.15 0.80 -0.10 0.15 0.15 -0.10 0.80 P= 1 1 1 0 1 1 - 1 0 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = JINO (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x...
step by step please Consider the following 2 -1 A = 0-2 -2 0 0 0,...
step by step please
Consider the following 2 -1 A = 0-2 -2 0 0 0, P- -1 0 1 -3 04 0 1 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (11, 12, 13) =(
2. (-12 points) DETAILS LARLINALG8 7.2.005. Consider the following. Toi-3 A = 5 - 1 0...
2. (-12 points) DETAILS LARLINALG8 7.2.005. Consider the following. Toi-3 A = 5 - 1 0 0 1 0 -6 4 - 4 P= 04 1 2 0 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = It (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues....
Consider the following A9 -24 (a) Verify that A is diagonalizable by computing P AP (b)...
Consider the following A9 -24 (a) Verify that A is diagonalizable by computing P AP (b) Use the result of part (a) and the theorem below to find the eigenvalues of A Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. Need Help?ReadIt Talk to a Tutor + -/1 points LarLinAlg8 7.2.005 Consider the following 0 13 A-10-201, P-1040 1 2 2 2-1 0 -4 2-4 (a)...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A =...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A = 040 P= 04 0 4 0 2 1 2 2 (a) Verify that A is diagonalizable by computing p-AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (91, 12, 13)...
please solve both 3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible)...
please solve both
3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible) a nonsingular matrix P such that p-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 8 -2 A= P= Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP = 1. [0/2 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.2.001. Consider the following. -11 40 A= -27 (a) Verify that A is diagonalizable by computing p-1AP. -1 0 p-1AP = 10 3...
Consider the following. 01-3 -5 2 0 1 2 2 6 -2 4 (a) Verify that...
Consider the following. 01-3 -5 2 0 1 2 2 6 -2 4 (a) Verify that A is diagonalizable by computing P1AP. (b) Use the result of part (a) and the theorem below to find the eigenvalues of A Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (A1, λ2, A3) Nood Holn2
8: Suppose that A and B are similar matrices, B = p-1AP, where 6 2 P...
8: Suppose that A and B are similar matrices, B = p-1AP, where 6 2 P = -1 1 We know that A and B have the same characteristic polynomial and the same eigenvalues. Suppose that 2 is one of the common eigenvalues and x = [4 1] is a corresponding eigenvector of A. Which of the following is the eigenvector of B corresponding to 2 ? "f1-4-0-0-0-0-01-10 #8: Select
Publish using a MatLab function for the following: If a matrix A has dimension n×n and has n line...
Publish using a MatLab function for the following:
If a matrix A has dimension n×n and has n linearly independent
eigenvectors, it is diagonalizable.This means there exists a matrix
P such that P^(−1)AP=D, where D is a diagonal matrix whose diagonal
entries are made up of the eigenvalues of A. P is constructed by
taking the eigenvectors of A and using them as the columns of P.
Your task is to write a program (function) that does the
following
If...
13-15 please! 13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1...
13-15 please!
13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
Consider the following. 1 -1 0 1 A= 1 -1 0-1 0.80 -0.10 0.15 0.15 -0.10 0.80 0.15 0.15 0.15 0.15 0.80 -0.10 0.15 0.15 -0.10 0.80 P= 1 1 1 0 1 1 - 1 0 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = JINO (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x...
step by step please
Consider the following 2 -1 A = 0-2 -2 0 0 0, P- -1 0 1 -3 04 0 1 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (11, 12, 13) =(
2. (-12 points) DETAILS LARLINALG8 7.2.005. Consider the following. Toi-3 A = 5 - 1 0 0 1 0 -6 4 - 4 P= 04 1 2 0 2 (a) Verify that A is diagonalizable by computing p-1AP. p-1AP = It (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues....
Consider the following A9 -24 (a) Verify that A is diagonalizable by computing P AP (b) Use the result of part (a) and the theorem below to find the eigenvalues of A Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. Need Help?ReadIt Talk to a Tutor + -/1 points LarLinAlg8 7.2.005 Consider the following 0 13 A-10-201, P-1040 1 2 2 2-1 0 -4 2-4 (a)...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A = 040 P= 04 0 4 0 2 1 2 2 (a) Verify that A is diagonalizable by computing p-AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (91, 12, 13)...
please solve both
3. [-12 Points] DETAILS LARLINALG8 7.2.007. For the matrix A, find (if possible) a nonsingular matrix P such that p-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 8 -2 A= P= Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. p-1AP = 1. [0/2 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.2.001. Consider the following. -11 40 A= -27 (a) Verify that A is diagonalizable by computing p-1AP. -1 0 p-1AP = 10 3...
Consider the following. 01-3 -5 2 0 1 2 2 6 -2 4 (a) Verify that A is diagonalizable by computing P1AP. (b) Use the result of part (a) and the theorem below to find the eigenvalues of A Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (A1, λ2, A3) Nood Holn2
8: Suppose that A and B are similar matrices, B = p-1AP, where 6 2 P = -1 1 We know that A and B have the same characteristic polynomial and the same eigenvalues. Suppose that 2 is one of the common eigenvalues and x = [4 1] is a corresponding eigenvector of A. Which of the following is the eigenvector of B corresponding to 2 ? "f1-4-0-0-0-0-01-10 #8: Select
Publish using a MatLab function for the following:
If a matrix A has dimension n×n and has n linearly independent
eigenvectors, it is diagonalizable.This means there exists a matrix
P such that P^(−1)AP=D, where D is a diagonal matrix whose diagonal
entries are made up of the eigenvalues of A. P is constructed by
taking the eigenvectors of A and using them as the columns of P.
Your task is to write a program (function) that does the
following
If...
13-15 please!
13. a 14. 15. 0 Find the eigenspaces of A = 0 1 -1 Then diagonalize A if you can. LO 0 1 b Determine values a, b, c for matrix A = 0 -2 c to be diagonalizable. LO 0 1) For nxn matrix A and B, true or false? a. A is diagonalizable if the sum of geometric multiplicities of the eigenvalues is n b. If A is invertible, the only real eigenvalues are 1 and...
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