Given two m ×m matrix X and Y , where XY = Y X. Suppose the eigenvalues of X are mutually different from each other and are real, and Y ̸= 0. Show that Y has the same eigenvectors as X and the eigenvalues of Y are real.

Q: find the eigen values and Of the matrix eigen vectors 2

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Q: 8 -3 0 7 9 2 -1 0 2 0 0 8 O O

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Q: 00 20 000 1 0 00 2 C = 2000 0 010 0100 y D = 0 200 1000

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Q: A = -53 -70 35 45

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Q: Find the eigenvalues of the given system of linear equations *; +3x, = 2x, 4x. +2x, = Ar, %3D

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Q: Find the eigenvalues and all possible Jordan forms if A 2 = zero matrix.

A: If A^2 = 0, then the characteristic polynomial of A is λ^2 = 0, which implies that the only…

Q: f(t) = t sinh 5t 5s 5s А. (s2-25)2 С. (s2 +25)2 10s 10s В. (s2-25)2 D. (s2 +25)2

A: We find the Laplace transform of  f(t)=tsinh(5t)

Q: 5 -1 0 -5 9 5 -1 0,

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Q: 4 2- i 9 A= |2+i 0 3 +i 3- i 7

A: According to the given information, it is required to find the eigenspace of the given matrix.

Q: All 2x2 matrix have 2 different eigenvalues True O False

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Q: 00 20 00 02 C = 2000 0001 0 010 0100 y D = 0 200 1000

A: let λ be an eigenvalue of C.

Q: Determine if v is an eigenvector of the matrix B -47 26 2 B = , v = -78 44 -5

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Q: find if the vector x is in the range for matrix A

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Q: If A be nxn matrix with eigen value L then find the eigen value of inverse of A .

A: The given matrix A be an n×n matrix with eigenvalue L. Calculate the eigen value of inverse of A.

Q: Consider the linear system 2 y' "' = [ _3__3] " ÿ. -5 -3

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Q: Select an Answer 1. -1 1 A = -2 0 ,v = 7 -6 1 -1 Select an Answer 2. 7 -2 12 -1 A = -8 1 -12 U = -4…

A: Here we have to determine if v is an eigenvector of the matrix A .

Q: Find the eigenvectors corresponding to each value of the matrix.

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Q: Find the three distinct real eigenvalues of the matrix

A: In this question, we have to find the eigenvalues of the given matrix. For this first, we find the…

Q: The trace and determinant of a 2 x 2 matrix are known to be -2 and -35 respectively. Its eigenvalues

A: solution :given that trace=-2and determinant =-35 of a 2×2 matrix .we know that trace =…

Q: Select an Answer v 1. зоо 4 A = 3 , v = 1 -3 -3 -6 3 Select an Answer v 2. -6 6 5 -1 A = -9 7 , v =…

A: We Know that  A is an “n × n” matrix and λ is an eigenvalue of matrix A, then x, a non-zero vector,…