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Let 4- 11 18 6 10 (a) Find the eigenvalues of A. (6) For each eigenvalue...
11 18 7 Let 4 6 10 (a) Find the eigenvalues of A. (b) For each...
11 18 7 Let 4 6 10 (a) Find the eigenvalues of A. (b) For each eigenvalue find the corresponding eigenvectors. (c) Let 21 and 22 be the eigenvalues of A such that 21 <12. Find a match for 11. Find a match for 12 Find a matching eigenvector vị for 11 - Find a matching eigenvector v2 for 12 Let P and D be 2 x 2 matrices defined as follows: 20 and P = [v1v2] o 22 that...
How to do Part 3? -- Find e^(At), the exponential of matrix A, where t ∈ ℝ is any real number.
How to do Part 3? -- Find e^(At), the exponential of matrix A,
where t ∈ ℝ is any real number.
Part 1: Finding Eigenpairs [10 10 5 10 -5 Find the eigenvalues λ,A2 and their corresponding eigenvectors vi , v2 of the matrix A- (a) Eigenvalues: 1,222.3 (b) Eigenvector for 21 you entered above: Vi = <-1/2,1> (c) Eigenvector for 22 you entered above: Part 2: Diagonalizability (d) Find a diagonal matrix D and an invertible matrix P D,...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6...
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12...
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12 -8 0 0 | 12 -7 -1 a) Eigenvalues: 4,4, -1; Number of independent eigenvectors: 2 b) Eigenvalues: 4,2, -1; Number of independent eigenvectors: 3 c) Eigenvalues: 4,-2,1; Number of independent eigenvectors: 3 d) Eigenvalues: 4,-2, -1; Number of independent eigenvectors: 3 e) Eigenvalues: 4,-2, -2; Number of independent eigenvectors: 2 f) None of the above.
(1 point) Let 3 -4 A = -4 -1 -4 -2 -2 If possible, find an...
(1 point) Let 3 -4 A = -4 -1 -4 -2 -2 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= II II D= Be sure you can explain why or why Is A diagonalizable over R? diagonalizable...
Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the...
Let matrix M = -8 -24 -12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP^−1. If not, explain carefully why not.
Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the...
Let matrix M = -8 -24 12 0 4 0 6 12 10 (a) Find the eigenvalues of M (b) For each eigenvalue λ of M, find a basis for the eigenspace of λ. (c) Is the matrix M diagonalizable? If so, find matrices D and P such that D is a diagonal matrix and M=PDP−1. If not, explain carefully why not.
-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 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11...
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
11 18 7 Let 4 6 10 (a) Find the eigenvalues of A. (b) For each eigenvalue find the corresponding eigenvectors. (c) Let 21 and 22 be the eigenvalues of A such that 21 <12. Find a match for 11. Find a match for 12 Find a matching eigenvector vị for 11 - Find a matching eigenvector v2 for 12 Let P and D be 2 x 2 matrices defined as follows: 20 and P = [v1v2] o 22 that...
How to do Part 3? -- Find e^(At), the exponential of matrix A,
where t ∈ ℝ is any real number.
Part 1: Finding Eigenpairs [10 10 5 10 -5 Find the eigenvalues λ,A2 and their corresponding eigenvectors vi , v2 of the matrix A- (a) Eigenvalues: 1,222.3 (b) Eigenvector for 21 you entered above: Vi = <-1/2,1> (c) Eigenvector for 22 you entered above: Part 2: Diagonalizability (d) Find a diagonal matrix D and an invertible matrix P D,...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12 -8 0 0 | 12 -7 -1 a) Eigenvalues: 4,4, -1; Number of independent eigenvectors: 2 b) Eigenvalues: 4,2, -1; Number of independent eigenvectors: 3 c) Eigenvalues: 4,-2,1; Number of independent eigenvectors: 3 d) Eigenvalues: 4,-2, -1; Number of independent eigenvectors: 3 e) Eigenvalues: 4,-2, -2; Number of independent eigenvectors: 2 f) None of the above.
(1 point) Let 3 -4 A = -4 -1 -4 -2 -2 If possible, find an invertible matrix P so that D = P-1 AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. P= II II D= Be sure you can explain why or why Is A diagonalizable over R? diagonalizable...
-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 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
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