[5 -31 12 * Given A = Find the eigenvalues and eigenvectors of matrix A

Q: 3 22 For the matrix A = 2 3 2 , the eigen vector corresponding to the eigen value d = 7 is 22 3.

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Q: (12 1 2 -4 (1) Find ab, where a & b are eigen values of a matrix A =

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Q: 12 6 j' -3 3 the eigenvalues and eigenvectors for the coefficient matrix. dy = and A2 %3D

A: The matrix given to us is  y→'=126-33y

Q: 4 -4 4 Find the eigenvalues and corresponding eigenvectors for the matrix at right if the…

A: Given matrix is A=4-4409-40-16. Corresponding characteristic equation is λ3-19λ2+110λ-200=0. To find…

Q: [2 3 4 Find the eigenvalues and eigenvectors of the matrix A = 0 Lo 1 -3.

A: GivenA=23402001-3To Findeigenvalues of A.

Q: 26. Find h in the matrix A below so that the eigenspace of A corresponding to λ = 4 is…

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Q: (VII). > Find the all eigenvalues and the corresponding eigenspace of matrix A, 2 0 0 where A=-1 1 3…

A: We need to find the eigenvalue and eigenvector for the given matrix. This can be done as follows:

Q: 2 -2 Find eigenvalues and corresponding eigenvector of the matrix F = I-2 -2 -1 3

A: Consider the given matrix F=2-202-21-223 Suppose λ be the eigenvalue of the given matrix, then the…

Q: [10 e eigenvectors of the matrix 1

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Q: -8 -10 15 -7 -9 7 -14 2. A = -3 Show that X, =-13 is an eigenvalue of the matrix A by finding its…

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Q: 1.37 (2 2) One of the eigenvectors of the matrix A=| is: 1 3

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Q: 3,-1,1 Show that the eigenvalues of the following matrix are [1 1 2] 4 1 5 Lo o 1]

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Q: 1 2 3] 2.104 The sum of the eigen values of the matrix given below is 15 1 3 1 1

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Q: [-1 0 01 1 2 1 Find the eigenvalues of A. Find a nonsingular matrix P and a diagonal matrix D such…

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Q: -2 2 Find the eigenvalues and eigenvectors of the matrix A 0 1 3 0 -4 d1 =, 51 = and and 13 v3

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Q: 3+i If the eigenvector of matrix A is then the eigenvector of A1 is: -i

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Q: [3 An eigenvector for value of 2 = -2 for the matrix 13 is A. В. С. D. E. None of the above A. O B.

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Q: [2 2 21 A = 2 2 3 Lo o 1 Find the Eigenvalues of the matrix A. .

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Q: 5 2 ? 0 5 What is the geometric multiplicity of the eigenvalue for the matrix

A: The given matrix is:5205To find the geometric multiplicities of eigenvalues

Q: 4 1 2 The value of p such that the vector 2 is an eigenvector of the matrix 1 14 -4 10

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Q: -2 5 Find the eigenvalues and associated eigenvectors of the matrix: 2 5

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Q: 2 1 1 2. Which one the following is an eigenvalue of the matrix 1 2 1 0 0 1 a) 4 b) -1 c) 0 d) 1

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Q: [2 3 4 3. Find the eigenvalues and eigenvectors of the matrix A = Lo %3D 2 1 -3.

A: To find- Find the eigenvalues and eigenvectors of the matrix A = 23402001-3

Q: 5 2 Which of the following is an eigenvector for the matrix? 3 6

A: Explanation of the answer is as follows

Q: 6. Find all eigenvalues and eigenvectors of the given matrix. 10 0 2 1 -2 3 2 1

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Q: 12. Let (2 1 1 A = 1 3 3 2 3 5 The eigenvalues of A are d1 = 1, 2, A3. Apply the deflation technique…

A: Given A=211133235and the eigen values of A are 1, λ2 ,λ3.

Q: 7 2 3 7 5 then, the number of 0 0 Let A = 7 linearly independent eigenvectors of A will be

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Q: 1 A) Consider the matrix A = | -1 1 Find the eigenvalues and eigenvectors of A.

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Q: 2 -21 Let A =|-2 -2 -6 6 -3. The Eigenvectors X corresponding to 2 = 3 are

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Q: 11-4 For the matrix 03 2 an eigenvector corresponding to the eigenvalue 3 is O A O B. О В. г2 3 O D.…

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Q: -8 – 15 -87 Find an eigenvector of the matrix 28 33 14 corresponding to the eigenvalue X = 3 - 39…

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Q: 1 The eigenvalues of the matrix A = 1 are O and 1 +1 and -1 +i and -i 1+i and 1-i

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Q: -1 Find the eigenvalues and eigenvectors of the matrix A = -3 -4 3 = and 12 =

A: We are given the matrix : A=-1-4-33 Let λ be the eigen values . A-λI=-1-λ-4-33-λ…

Q: 3 5 Find the eigenvalues and eigenvectors of the matrix A = 3 1 and V2 = ||

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Q: -1 0 431 -1 2 0 -1 11 1: Find the Eigen-values and eigenvectors of matrix A:

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Q: Find the Jordan canonical form of each matrix

A: Given: The Jordan canonical form of each matrix is given below as,

Q: 2. Let (2 2 -2 A = | 5 1 1 5 -3, -3 a. Compute e4 using the definition of the matrix exponential. b.…

A: The given matrix is: A=22-251-315-3 a) Find the matrix eA using definition of matrix exponential.…

Q: [: [: ] -5 If vi = and v2 = -5 are eigenvectors of a matrix A corresponding to the eigenvalues X1 =…

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Q: 3. Find the eigenvalues of the matrix [i 0 3 A = |3 2 1 2 01

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4 0 The matrix A = 0 -2 has eigenvalues :

A: See in the next step

Q: 1. The matrix A is given by 2 4 A = 3 1 -1 -4 1 (a) Find the eigenvalues and a corresponding set of…

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Q: 2 22 1 For the matrix A=| 2 2 2 an eigenvalue corresponding to the eigenvector v= 1 is A = 2 22

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Q: 3 4 2 -1 6. | Find all eigenvalues for the matrix D = 5 0 -2 5 76 N

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Q: -1 Find the eigenvalues and eigenvectors of the matrix A 0 10 and and

A: Given: 5-16050-1010

Q: 6. If A = 8 is an eigenvalue of the matrix 4 8 ,then the corresponding eigenvector is=. Select one:…

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Q: [5 9] Find the eigenvalues and eigenvectors of the matrix A = |1 5 A1 = A , v1 and

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Q: (e). Find all values of x for which the matrix 1 A 4 has an eigenyalue equal to 5.

A: We can use cayley Hamilton theorem to find value of x

Q: [2 2 3 3] 1 1 The number of distinct eigenvalues of the matrix A = is equal to 0 0 33 0 0 0 2

A: Remark: A eigenvalue of a matrix is a root of its characteristic polynomial.  The product of the…

Q: -2 5. Find eigenvalues and eigen spaces of the matrix A = -1 1 -3 2

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.