Obtain the Controllable Canonical Form of a 4x4 matrix if its eigenvalues are given as: a) 0, -1, -2, +3 b) -1, -1, -2, +3 с) -1, -1, -1, 3

Q: If the eigen vectors of a 2 x 2 matrix A corresponding to the eigen values –1 and6 are 2…

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Q: Find a condition on a and b, such that the symmetric matrix A %3D has only ositive eigenvalues

A: In the given question we have to find the condition on a and b, such that the symmetric matrix has…

Q: Show that the matrix is skew – Hermitian and hence find the eigen Values and eigen vectors

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Q: Give an example of a rank 1 matrix A such that the vector 3 v = 1 is an eigenvector.

A: Need to find rank 1 matrix

Q: Prove that if A is an upper (lower) triangular matrix, then the eigenvalues of A are the elements on…

A: Given:                A is an upper(or lower) Triangular Matrix :   To prove:…

Q: In Exercise, find a symmetric 2X2 matrix with eigenvalues λ 1and λ2 and corresponding orthogonal…

A: Let A= abcd be the required 2 x 2 matrix. Given: Eigenvalues: λ1=3 , λ2=-3

Q: Determine if the following statement is true or false, and explain why: If an n x n matrix is…

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Q: If A is a 3 x 3 matrix which has eigenvalues 2 = 1, a Then A is diagonalizable 2, and 2 = –3. False…

A: 7. As if in a matrix all the eigen values are distinct then the matrix must be diagonalisable.

Q: If the matrix Anxn does not have n different eigenvalues, then it does not have n linearly…

A: To tell - If the statement is true or false.

Q: The minimum of the three eigen-value of the given matrix is: 1 -1 A = -1 0 0 -2

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Q: Evaluate the Eigen Value and Eigen Vectors of the following system 1 -1 -6 -2 5 4

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Q: Show that a matrix of the same size but with no eigenvalues that are real is similar to the matrix:…

A: Let us consider a n×n matrix. we know that Characteristic polynomial of an n×n matrix A is degree n…

Q: Let A be an eigenvalue of an square matrix A. Show that:

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Q: Prove that the eigenvalues of an upper triangular matrix M are the diagonal entries of M.

A: Given that M is an upper triangular matrix of order n, then

Q: Let A be a 5 × 5 matrix with 3 eigenvalues

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Q: Find a 2 x 2 matrix A such that [14]. are eigenvectors of A with eigenvalues 9 and -1, respectively.…

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Q: Let A be a 5x5 matrix and let 1 be an eigenvalue of multiplicity 4. If the rank of A-AIis 2, explain…

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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: Find all the Eigen values and a basis of each Eigen space of the matrix ´1 1 -1] -1 3 -1 -1 2

A: The given matrix is  A=11-1-13-1-120 Finding the eigen values…

Q: Compute the eigenvalues and bases of eigenspaces of the following matrix -2 1 4 4 1 -4 -1 1 A = 3

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Q: Let A be a Hermitian matrix. Show that all its eigenvalues ​​belong to the real axis.

A: See proof below

Q: If the eigen vectors of a 2 x 2 matrix A corresponding to the eigen values -1 and6 are and…

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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: Find a basis of the eigenspace associated with the eigenvalue 1 of the matrix -1 0 2 4 A = 1 -7 -3…

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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: 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: Let A be an anti-Hermitian matrix. Show that all its eigenvalues ​​belong to the imaginary axis.

A: We must know that all the eigen values of a hermitian matrix are always real.

Q: Let A be an idempotent matrix (that is, A2 = A). Showthat A = 0 and A = 1are the onlypossible…

A: Let A be an idempotent matrix (that is, A2 = A). Show that A = 0 and A = 1are the only possible…

Q: What is the set containing all the eigenvectors of the matrix 2. {[:} 2 -1

A: The eigenvalues of any matrix are given by the values of λ for which det (A-λIn) = 0. The given…

Q: If A is an nxn matrix, then the eigenvalues can be determined by

A: Given that if A is an n×n matrix, then our aim is to tell how eigen valuescan be determined?

Q: Show that if a matrix U is both unitary and Hermitian then any eigenvalue of U must equal either 1…

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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: Find the eigenvalues and eigenvectors of the matrix A = 10] -1 -2 and || ||

A: Let's find .

Q: Find the eigenvalues of the triangular or diagonal matrix.

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Q: Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are…

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Q: Show that the eigenvalues of the upper triangular matrix are λ = a and λ = d, and find the…

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Q: An eigen vector of the matrix A = is 0 1

A: Let A be  matrix. Solve the equation, A-λI for λ to calculate the eigen value(s). Use the eigen…

Q: Find a 2 × 2 matrix A such that the entries of A are all real numbers and -4 is an eigenvalue of A²,…

A: We can use the following results: 1. The eigenvalues of a matrix B are solutions of the equation…

Q: The diagonal elements of a 3x3 matrix are 2, 1, –3 are respectively. If two of its eigen values are…

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Q: If A and B are row equivalent matrices, do they necessarily have the same eigenvalues? Either prove…

A: If X and Y are row equivalent matrices, then the rows of the matrix X can be derived from the rows…

Q: Find a 2x2 matrix A that has two eigenvalues 4, -1 whose eigenvectors -3 and -1 1

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Q: Construct a 3 x 3 symmetric matrix A such that the eigenvalues of A are 1 with multiplicity two and…

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Q: Find the eigen Valnes and eigen Vectors of the matrix A = 5 7 -5 4 - 3

A: We have to find the eigenvalues and eigenvectors for the matrix A=57-504-128-3.

Q: Let A be the 2 x 2 matrix with elements a,, a12 = a21 = + 1 and a,, = - 1. Then the %3D eigenvalues…

A: Introduction :Given , a matrix A with elements and we have asked for the eigen values of matrix A19

Q: There does not exist a 3 x 3 matrix A with eigenvalues a 3, -3 +i, -2 i. Select one:

A: We have to consider the given condition

Q: Let A be the matrix A = ( 1 -2 -1 -6 0 a) Find all eigenvalue and coresponding eigenvector of A;

A: Explanation of the solution is given below...

Q: Find the three distinct real eigenvalues of the follwoing matrix

A: To Find the three distinct real eigenvalues of the follwoing matrix