Suppose B is a 6 x 6 matrix with eigenvalues A= 2, 2, 2, 2, 2, 2. If it is known that (B- 21) = 0 but (B-21)2 #0, write down all possible Jordan canonical forms for B.

Q: If X is a rankr matrix, show that the two square matrices XXH and X#X have the same nonzero…

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Q: Given that for matrix A= 4 -2 1 5 3 14 Eigenvalues are 4, 1. Find its eigenvectors

A: Given matrix is: A=400-210534 Given matrix is diagonal matrix therefore, eigenvalues are 4 and 1.…

Q: If A is a 3 x 3 matrix such that A' = - A, then 0 is an eigenvalue of A %3D Select one: True False

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Q: Suppose A is n x n matrix and it has at least one real eigen value, then n must be an even number.…

A: Here we describe atleast one real eigenvalue for n×n matrix.

Q: If 2 is one of the eigen vector of a matrix A = |1 ] A3x3 has three distinct eigen values then which…

A: INTRODUCTION: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue -3 + 5¿ with [-5+3i]…

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Q: Let A be a 2x2 matrix such that Tr(4) =10 and det(A) = 16. Then which of the following are the…

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Q: A be an orthogonal n by n real matrix where n is an odd number. Show that 1 or -1 must be an…

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Q: Suppose the matrix, A, has eigenvectors and whose eigenvalues are 4, -5 and -2 respectively. Then,…

A: Matrix P can be written as linear independent eigenvectors. and MATRIX D, diagonal matrix whose…

Q: Consider the following matrix: 1 1 A = -2 0 2 -1 If -1 is an eigenvalue of A, what is the value for…

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Q: For n xn matrices A and B with B invertible AB and BA have the same eigenvalues. Select one: O True…

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Q: If A is a 5 × 5 real matrix with trace 15 and if 2 and 3 are eigenvalues of A, each with algeraic…

A: Solution: Given  A is 5×5 real matrix  and trace(A)=15  and we have to find det(A)

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: Suppose that X is an eigenvector of a matrix A with corresponding eigenvalue 3. Then X is an…

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Q: Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue 9-3i with corresponding…

A: If x+iy is an eigen value of a matrix then x-iy is also an eigen value of the same matrix. To find…

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 4 x 4 matrix A has eigenvalues A₁ = 1,1₂ = -4,13 = 7, and A4 = - 7. Use the following…

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Q: Suppose B = XAX2, where X is the eigenvector matrix of B and A is its eigenvalue matrix. Compute the…

A: Please check step 2 for the solution.!

Q: If A, B are n xn matrices, suppose A and B have the same eigenvalues A,,A,...A, with n linearly…

A: We have to check

Q: Suppose A is a 4X3 matrix whose elements are all 1's. What are the eigenvalu- Select one: O a. (3,…

A: Suppose A is 4×3 matrix whose elements are all 1's.  What is the eigenvalues of AAT?

Q: Suppose that A is a matrix such that A2=0. Show that every eigenvalue of A is equal to 0.

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Q: If A is 4 x4 matrix with 4 linearly independent eigenvectors then A is diagonalizable. Select one: O…

A: If A is 4 x 4 matrix with 4 linearly independent eigenvectors  To determine A is diagonalizable

Q: Suppose that A is a 3 x 3 matrix with eigenvalues 1 = -2, 1, 1. Show that A- =(315 (3l3 – A²). %3D

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Q: Suppose that a 4 x 4 matrix A has eigenvalues ₁-1,A2-6, 3-7, and 14--7. Use the following method to…

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Q: If A is 3 x 3 matrix with eigenvalues A= 4,4,3 , then A is defective. Select one: O True False

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Q: Let A be an nxn matrix. Explain why the eigenvalues of A and Ať are identical.

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Q: If A Is a 3 x 3 matrix which has eigenvalue 2 10, 2 = -2, and 2 = -3. Then A is diagonalizable %3D O…

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Q: Suppose B is a diagonalizable matrix and the only eigenvalues of B are −1 and 1. Prove that B is…

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Q: 2) Let A is 2 x2 matrix with 4 and -3 eigenvalues and suppose that is an eigenvector for the value 4…

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Q: 2. Determine whether there exists a 3 x 3 symmetric matrix whose eigenvalues are A1 = -1, A2=3, A3 =…

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Q: The eigenvalues of a 4 x 4 matrix A are given by 2,-1,5,-4, then det(A)=

A: Given:-  The eigen value of a 4×4 matrix A are given by 2,-1, 5,-4To find:- det A=?

Q: 3 Suppose the matrix, A, has eigenvectors -2 , - 12 and whose eigenvalues are 9, 7 and 0 1…

A: We have to find the matrix P and D.

Q: Suppose A is a matrix with eigenvalues A1 = 1, A, = 2, A3 = -3, with corresponding eigenvectors v1…

A: Given: A is a matrix with eigenvalues λ1=1, λ2=2, λ3=-3 with corresponding eigenvectors v1=001,…

Q: A=

A: The given matrix,  A=8k6-6

Q: If А, ВЕ Мnхn (R) are symmetric matrices with all negative eigenvalues, then A + B has all negative…

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Q: Is the following statement correct? Suppose A is a 3 × 3 matrix having eigenvalues −1, 1, 2.  Ak is…

A: The given matrix of order A (3×3) The eigen values are   - 1, 1, 2

Q: Suppose that A is symmetric matrix which has eigenvalues -1, 0 and 1 and corresponding eigenvectors…

A: We have to determine a matrix P which orthogonally diagonalizes A and compute A100.

Q: IfA lis a real symmetric matrix with eigenvalues A= 5 and 2= 6, with respective eigenspaces E, =…

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Q: Suppose that A is an n×n matrix with n eigenvalues μ1, μ2, ..., μn. Show that the determinant of A…

A: Consider the provided question, We have to show that determinant of matrix A is equal to the product…

Q: If A is 3 x3 matrix with eigenvalues = - 1,1,4 , then A is invertable. Select one: O True O False

A: True

Q: If A is 3x3 matrix with eigenvalues A=4,4,3, then A is defective. Select one: O True O False

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Q: If A is a 3 x 3 matrix such that AT = - A, then 0 is an eigenvalue of A Select one: O True False

A: A is a 3×3 matrix such that AT=-A.

Q: Find eigenvector for 2 = 3 and given matrix A. X2= x3 Submit the Answer 2 Question 2 grade: 6. 5 3 A…

A: To find the eigenvector corresponding to eigenvalue 3 for the matrix: A=653101710−5−11−2

Q: Suppose A> 0 and u are a pair of eigenvalue and eigenvector of a 2 x 2 matrix A and v = Au. Then v…

A: we have to find the True and False. for given statement λ>0 ,u are eigenvalues and eigenvectors…

Q: The matrix A: = has two distinct real eigenvalues if and only if k> 25

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Q: If A is 3 x3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: C True False

A: If A is 3 × 3 matrix with eigenvalues λ = 4, 4, 3  Then,  A is defective  We have to tell it is true…

Q: Does there exist a symmetric matrix with eigenvalues 11 =1 and 12 = 3 and eigenvectors V1 = and v2…

A: Symmetric matrix A=AT Let  A=abbd We know PAP-1=D P is an invertible matrix of eigen vectors Dbe…

Q: ) Suppose that the squared matrix A is symmetric and all its eigenvalues are (a) different. Show…

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Q: two nxn symmetric matrices A and B=A+AA, if of A and B₁ ≤ B₂ ≤ ≤ Bn are the eigenvalues of ..

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Q: For nxn matrices A and B with B invertible AB and BA have the same eigenvalues. Select one: O True O…

A: The eigenvalues of product of two n*n square matrices will have same Eigen values.