4.5 8 -4 2 -4 is an eigenvector of 4 2 , the eigenvalue corresponding to the eigenvector is 0 -2 If 1 -4 a) 1 b) 4 c) -4.5 d) 6

Q: Give the eigenvalues of 4 -3 -6 1 1 - 1 - 1 (Hint: 2 is an eigenvalue.) а) О (-3, 1, 2) b) O {-2, 1,…

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Q: One of the following is an eigenvector of A = 14 that corresponds to the eigenvalue A=2 none 2

A: The given matrix is, A=1402 The eigen values are calculated as, A=1-λ402-λ The determinant is,…

Q: 1. If å is an eigenvalue of a matrix A, prove that 1' – 52 is an eigenvalue of the matrix A – 5A.

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Q: 31. Show that if A is an eigenvalue of a matrix A, then A2 is an eigenvalue of A?.

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Q: 1 Show that if 2 is an eigenvalue of A, then - is an eigenvalue of A-1.

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Q: 3) Let C = λ = 4 0 0 0 -1 -46 -200 2002 5 2 10 44 2 -2 The eigenvalues for C are:

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x, = (1, 2,…

A: Note: Let A be a square matrix and x be an eigen value of A. A non-zero vector V is said to the…

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A: Explanation of the answer is as follows

Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 1q = 13, x, = (1,…

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Q: 8) Suppose V is finite-dimensional, T E L(V) had dim V distinct eigenvalues, ar SE L(V) has the same…

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Q: Is A 1 an eigenvalue of to perform row reduction. 4 0 1 -2 3 3 ? If so, find one corresponding…

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Q: If v, and v, are linearly independent eigenvectors, they correspond to distinct eigenvalues. True O…

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Q: -5 -7 Let A = %3D -1 k For A to have 0 as an eigenvalue, k must be

A: We  have  A  as a matrix and eigen value 0 ,  Using characteristic equation,        |A- λI| =0 we…

Q: 4) provet hat if A and B ave two square matnbes of degree n and IAl+ then As and BA have the same…

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Q: A, IS an eigenvalue ofA and that X; Is a corresponding eigenvector. 1 = 5, x, = (1, 2, –1) 12= -3,…

A: The given matrix is A=-22-321-6-1-20 the characteristic equation is A-λI=0…

Q: 4 2 Find an eigenvector corresponding to the eigenvalue 6 of the mat rix [15 O B. OD. O E.

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Q: Let A 2 4 4 0 1 -1 0 1 3

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Q: 6. Show that the function Ae ax is an eigenfunction of the operator d? What is the -ах dx2…

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. A = 13, x, = (1, 2,…

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Q: 2 31 Find the eigenvalues A of the mat rix0 1 4 0 0 5] O A. 1 = 1, 4, 5 овА 3D 1, 2, о OC.A= 3, 1, 0…

A: Option D is correct  For lower triangular matrix, eigen values are trace of the matrix

Q: 4 Let A 1k For A to have 0 as an eigenvalue, k must be

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Q: 4 – 14 Suppose u Au -2 and A?u 1 -3 Then A has eigenvalues A =

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 1 1 = 2, x, = (1,…

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Q: 2. Show that is an eigenvalue of A and find one eigenvector corresponding to this eigenvalue. 1 0 21…

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Q: Exercise 2. 1) If A E M3x3(F) has 1,2 and 3 as E(3, A)? eigenvalues, what is the dimension of

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

Q: Find the eigenvalue and eigenvector of the matr 20-27 0 4 -2 0

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Q: Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = (1,…

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Q: Given that vi = (-2, 1) and v2 = (1, 1) are eigen- vectors of -5 =[]. A = determine the eigenvalues…

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 5, x, = (1, 2,…

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Q: 1) Prove that if both Tw and T then T is diagonalizable. are diagonalizable and have no common…

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Q: 3 Suppose that A = Find the eigenvalues of A, i.e. the A 1 4 which satisfies det|A – AI2| = 0.…

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

Q: If A=PDP-, where P 13 and D= 24 20 03 find an eigenvector v corresponding to eigenvalue A= 3 with [1…

A: The answer is given as follows.

Q: erify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. 2 -3 1 -6 11 = 5, x1…

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Q: Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = (1,…

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Q: Suppse that A ie 4x6 and the eigenvaluas of A'A are 3,2,1,0,2 and o listed with multiplicrties, What…

A: We have to find the rank of A.

Q: -4 -5] Let A = -8 k For A to have 0 as an eigenvalue, k must be

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Q: 4 -1 .Verify that 5 is an eigenvalue of A and v is an eigenvector. Then 4 -1 -1 -1 4 orthogo¬nally…

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Q: 8) Suppose V is finite-dimensional, T E L(V) had dim V distinct eigenvalues, and S E L(V) has the…

A: As given by the question There are given that the v is finite-dimensional. And, The distinct…

Q: Show that if T : Rº → Rº has 6 distinct eigenvalues and S has the same eigenvectors as T, then ST =…

A: The solution of given problem is followed by

Q: 5. Prove that: If A has an inverse, then it has no eigenvalues of 0, and If there is no reciprocal…

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Q: 1 11 2 determine the eigenvalues of the matrix A and an 1 2 Q4: If A.x = Ax, where A = 1 3. 1…

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Q: Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 13, x1 = (1,…

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Q: fA, =4 is an eigenvalue for A4x4 With algebriac multiplicity =3, and A, = 2 %3D is another…

A: We know if λ1,λ2.…,λn are eigenvalues of a n×n  Matrix A then  det(A)=λ1.λ2.........λn Given that…

Q: 14 4 13 Find the eigenvalues of A, given that A = -7 -3 -7 -10 -4 -9 -1 -1 3 and its eigenvectors…

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Q: Show that if 2 is an eigenvalue of A, then is an eigenvalue of A-1.

A: We have  to prove if λ is an eigenvalue of  A  Then 1/λ is an eigenvalue of A^-1

Q: Linear algebra problem

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Q: If -1 -2 -1 A = 1 3 then what is a 3-eigenvector of A?

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Q: 3 5 6 4. Let A 0 2 h What should be the value of h so that the dimension of the eigen 0 0 2 space…

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Q: Is λ=4 an eigen value of [ 3 0 −1 2 3 1 −3 4 5 ] ? If so, find one corresponding eigen vector?

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.