Homework Answers
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3,...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A ...
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.
5. Find a 2 x 2 matrix A such that A2 = I2, but A +...
5. Find a 2 x 2 matrix A such that A2 = I2, but A + +12. (Hint: you can do this algebraically, or geometrically.) For all the remaining questions, let n > 2 and let A and B be n x n matrices. 6. Does the equation A(B – In) + (In – B)A = On,n always hold? Either prove it or give a counter-example. 7. If A and B are invertible, does that imply that AB is invertible?...
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A =...
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A = 18] (The 3 -7 same as in the previous problem.) di = 2, V1 = [1] and 12 = -1, V2 = - [11] [1] 3 21 = 1, V1 = ܒܗ ܟܬ and 12 = -2, V2 = 2 x = 1, V1 = and 12 = -2, V2 = [11 11 x = -2, Vi and 12 = -3, V2 [1]
Consider a certain 2 x 2 linear system - Air, where A is a matrix of...
Consider a certain 2 x 2 linear system - Air, where A is a matrix of real numbers. Suppose at least one of its nonzero solutions will converge to (0,0) ast - 00 Which of the following statements is consistent with this. Choose all that apply. A has eigenvalues 11 = -3, 13 = 1 The phase portrait looks like this: The origin is a stable node • Previous Next
Explain how to find the eigenvalues of the following 2 x 2 matrix: -11 40 -27
Explain how to find the eigenvalues of the following 2 x 2 matrix: -11 40 -27
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
Suppose that the matrix A A has the following eigenvalues and eigenvectors: (1 point) Suppose that...
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Consider the 2×22×2 matrix AA given by A=[−3−2029].A=[−32−209].. (2/10) Find the eigenvalues λ+λ+ and λ−λ−, larger...
Consider the 2×22×2 matrix AA given by A=[−3−2029].A=[−32−209]..
(2/10) Find the eigenvalues λ+λ+ and λ−λ−, larger and smaller or
equal or conjugate, respectively, of the matrix AA,
The last part of the problem I can't seem to get.
(10 points) -3 2 Consider the 2 x 2 matrix A given by A = - 20 9 a. (2/10) Find the eigenvalues l_ and __, larger and smaller or equal or conjugate, respectively, of the matrix A, d. = 3+2i Σ...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
(1 point) The matrix 2 -1 0 A2-3 -1 has three distinct real eigenvalues if and only if
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.
2. A 5 x 5 matrix of real numbers, A s found to have the following eigenvalues (a) Explain why A is, or is NOT, diagonalizable. (b Explain why A is, or is NOT, inzertibie.
5. Find a 2 x 2 matrix A such that A2 = I2, but A + +12. (Hint: you can do this algebraically, or geometrically.) For all the remaining questions, let n > 2 and let A and B be n x n matrices. 6. Does the equation A(B – In) + (In – B)A = On,n always hold? Either prove it or give a counter-example. 7. If A and B are invertible, does that imply that AB is invertible?...
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A = 18] (The 3 -7 same as in the previous problem.) di = 2, V1 = [1] and 12 = -1, V2 = - [11] [1] 3 21 = 1, V1 = ܒܗ ܟܬ and 12 = -2, V2 = 2 x = 1, V1 = and 12 = -2, V2 = [11 11 x = -2, Vi and 12 = -3, V2 [1]
Consider a certain 2 x 2 linear system - Air, where A is a matrix of real numbers. Suppose at least one of its nonzero solutions will converge to (0,0) ast - 00 Which of the following statements is consistent with this. Choose all that apply. A has eigenvalues 11 = -3, 13 = 1 The phase portrait looks like this: The origin is a stable node • Previous Next
Explain how to find the eigenvalues of the following 2 x 2 matrix: -11 40 -27
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
Suppose that the matrix A A has the following eigenvalues and
eigenvectors:
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 2 = 2i with v1 = 2 - 5i and - 12 = -2i with v2 = (2+1) 2 + 5i Write the general real solution for the linear system r' = Ar, in the following forms: A. In eigenvalue/eigenvector form: 0 4 0 t MODE = C1 sin(2t) cos(2) 5 2 4 0 0...
Consider the 2×22×2 matrix AA given by A=[−3−2029].A=[−32−209]..
(2/10) Find the eigenvalues λ+λ+ and λ−λ−, larger and smaller or
equal or conjugate, respectively, of the matrix AA,
The last part of the problem I can't seem to get.
(10 points) -3 2 Consider the 2 x 2 matrix A given by A = - 20 9 a. (2/10) Find the eigenvalues l_ and __, larger and smaller or equal or conjugate, respectively, of the matrix A, d. = 3+2i Σ...
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