Determine whether the following matrix is diagonalizable. Justify your answe. (First find the characteristic equation and the eigenvalue of the matrices) 4 2 а. -5 4 4. 3 4 2 5 6 3 3 2 1 b.

Q: If λ is an eigenvalue of a matrix A, prove that λ3−5λ is an eigenvalue of the matrix A3−5A

A: Given: eigen value of a matrix A is λ. By definition of eigen value Ax=λx…

Q: Let 4 1 A = | 2 3 2 1 0 4 (a) Find the eigenvalues of A. (b) For each eigenvalue 2, find the rank of…

A: Given matrix is 401232104. a We have to find the eigenvalues of A. The eigenvalues of A are the…

Q: Find the eigenvalues and normalised eigenvectors of the following matrix. 1 0 0 1 5 – 10 - A = 1 2 1…

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Q: Suppose A SAS1, then the eigenvector matrix of A + 41 is %3D O a S+ 41 Ob. S OcS+I d. S-41

A: We will find the diagonal matrix corresponding to the matrix, A+4I

Q: If A is a 3 x 3 matrix with eigenvalues 2,-2,1. Let 8 = A - 3A2 Then det(B) = -160 Select one: True…

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Q: Let A be 3 x 3 matrix with eigenvalues 3,-2,, let B = A-2 + I, then the eigenvalues of B are 10 B)…

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Q: 2 7 A = -1 -6

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Q: find all eigenvalues and eigenvectors of the given matrix.17.(1√3√3−1)

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Q: Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 4 A1 = 1= A2 = 3 =…

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Q: Suppose ?<0λ<0 and ?u are a pair of eigenvalue and eigenvector of a 2×22×2 matrix ?A and ?=??v=Au.…

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Q: Calculate the positive eigenvalue and a corresponding positive eigenvector of the Leslie matrix L.

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Q: Find the eigenvalues and their associated eigenvectors of the matrix A below. 3 A -2 3 8

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Q: Let A be a 3 x 3 matrix with eigenvalues 7/2, 7//4, 7/8. If the eigenvalues of A- are A1,2, 13, then…

A: we have given eigen values of matrix A these are 7/2,7/4,/7/8 As we know eigen value of A-1 =1/lemda…

Q: 2 2 A = 1 2 1 1 1

A: Solution:-

Q: Let A be 2 x2 matrix, A has -1,2 as an eigenvalues and the corresponding eigenvectors, respectively.…

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Q: Suppose that A is a square matrix satisfying A5 = 0. What can you say about the eigenvalues of A?…

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Q: Which of the following values is an eigenvalue of the below matrix: 3 1 4

A: Given : 3214

Q: Find eigenvector for 2 = 2 and given matrix A. X2= X3= Submit the Answer 2 Question 2 grade: 6. 3 A…

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Q: It is possible for a 3 x 3 matrix A with eigenvalues a = 3,-3 + i, -2 + i. Select one: O True O…

A: A 3x3 matrix has maximum 3 different Eigen values possible.

Q: If A is 3 x 3 matrix with eigenvalues 0, 2, 3. Then: | a. |AA"| = 0 а. O b. |AA"|= 6 %3D c. |AA"| =…

A: See solution below.

Q: Consider the following matrix A - 4-3 -2 Lnd the eigenValues, eigenvectors

A: 1st we will find Characteristic  polynomial  and then find eigen values by equating it with zero .…

Q: Given a matrix A with eigenvalues λ1,···,λn, calculate eigenvalues of the following matrices (show…

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Q: 1. Without actually setting up any equations, write down the eigenvalues of the following matrix: 1…

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Q: Find the matrix B given its eigenvalues d, = -1 and 1, =3 and the corresponding eigenvectorsy…

A: Using property of eigen values and eigen vectors we can find correct matrix

Q: 2. Determine whether there exists a 3 x 3 symmetric matrix whose eigenvalues are A1 = -1, 2= 3, A3 =…

A: Introduction: A diagonal matrix is one that only has non-zero values on its major diagonal. To put…

Q: Let A be 2 x 2 matrix, A has -1,2 as an eigenvalues and the corresponding eigenvectors,…

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Q: Let A be 2 x 2 matrix, A has -1,2 as an eigenvalues and the corresponding eigenvectors,…

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Q: Find the characteristic equation and the eigenvalues of the matrix 3 2 A= [ 1 3 -2

A: Solved below.

Q: 2. Diagonalize the following matrices, if possible. The real eigenvalues for (b) are given. В 11 (a)…

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Q: Find eigenvector for 1 = 2 and given matrix A. X2= X3= Submit the Answer 2 Question 2 grade: 6. 3 A…

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Q: Q4. Find the eigenvalues and associated eigenvectors for the given matrices. -2 -4 2 B = (-2 1 2 4…

A: Eigenvalue is calculated using characteristic polynomial. Characteristic polynomial  is given by…

Q: Find the 2 x 2 matrix A that has the eigenvalues and eigenvectors (6) . 6) A1 =1 = A2 = -1

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Q: If A is a 3 × 3 matrix which has eigenvalues 2 = -11, 2 = 2, and 2 = 5. Then A is diagonalizable…

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Q: Find the eigenvalue and eigenvector for the matrix -2| 1 2 A = 1 1 1 -1

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Q: Consider the matrix 2 2 A = 2 4 2 2 2 (a) Compute the eigenvalues and eigenvectors of A. ||

A: An eigenvector , corresponding to a real nonzero eigenvalue, points in a direction in which it is…

Q: (b) Explain why we must have that det(S – A,I) = 0 for each of the eigenvalues of S, where I is the…

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Q: Determine whether X = is an eigenvector for the 2 x 2 matrix 8 2 A = 2 5 If it is an eigenvector,…

A: Solution as follows

Q: For the given matrix and eigenvalue, find an [-13 2] eigenvector corresponding to the eigenvalue.…

A: As Many Questions are given , I will solve Only the first One:

Q: : Find the eigenvalues of the Matrix: c = (; ) 2 1 0) -3 %3D

A: We will first find the characteristic equation, whose roots are the eigenvalues.

Q: 3. Find the eigenvalues and normalized eigenvectors of the following matrix. 2 0 3 050 30 2

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Q: 4. For the given matrix -2 1 3 1 3 -1 3 1 2 a) Use the direct method to find all the eigenvalues and…

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Q: Find a 3 x 3 matrix A that has eigenvalues A = 0, 8, - 8 with corresponding eigenvectors 1 1 -1 1 -1…

A: If u1, u2,u3 are eigenvectors with a,b,c as corresponding eigenvalues, the base matrix Acan be…

Q: Calculate the positive eigenvalue and a corresponding positive eigenvector of the Leslie matrix L.

A: Consider the following matrix: L=020.50 Subtract λ from the diagonal elements of matrix: 0-λ20.50-λ…

Q: What is the set containing the eigenvalues of the matrix 1 a) O {1,0} b)O {1,2} c)O {2,0}

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Q: If A is a 3 × 3 matrix which has eigenvalues 2 = 1, a = 2, and 1 = -3. Then A is diagonalizable %D

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Q: Given a matrix A with eigenvalues λ1,···,λn, calculate eigenvalues of the following matrices (show…

A: Solution

Q: 9. Determine which of the following vectors 1 -1 is an eigenvector of the matrix -- 1 1 1 1 -1 1 -1…

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Q: Calculate the positive eigenvalue and a corresponding positive eigenvector of the Leslie matrix L.

A: The given matrix is, L=11.50.50 The objective is to find the positive eigenvalue and corresponding…

Q: 7 Find the matrix, A, with eigenvectors -11 and 12 whose eigenvalues are 5 and 2 respectively. 19 A…

A: to find:- Matrix A.