(i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii) For A = [0 3 6: l, verify that tr(A'A) = tr(AA').

Q: 0 1 1 1 0 0 1 1 1 0

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A: Matrix decomposition.

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

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Q: snip

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A: See the detailed solution below.

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A: Please check step 2 for the solution.!

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A: Given: λ1=2λ2=4v1=1-1v2=22 Calculation: Compute the matrix A as follows. v=12-12 and λ=2004

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Q: Q2. (a) Find the eigenvalues and corresponding eigenvector of the matrix [-2 5 4 5 4 5 -2| in

A: For eigen value , first we subtract λ from the digonal entries of the matrix    A=-25457545-2

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Q: Find all of the eigenvalues of the matrix A over the indicated Zp.

A: Find all of the eigenvalues of the matrix A over the indicated Zp. A=2112

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A: E-1=Span-21E3=Span5-3 let v1=-21v2=5-3

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Q: For matrices A and B with B invertible AB and BA have the same eigenvalues.

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A: Given a matrix, x'=9454α94x To determine the eigen values, consider 94-λ54α94-λ=94-λ2-54α

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Q: prior to Exercises 15–18 in Section 3.1. [Note: Finding the characteristic polynomial of a 3 x 3…

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A: NOTE: Refresh your page if you can't see any equations. . write both eigenvalues in the diagonal…

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

A: True

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Q: It is possible for a 3 x 3 matrix A with eigenvalues 2 = 3,-3+i,-2+i. 10

A: Need to find true false

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A: Eigen values of A are -1 and 2 .  Also,  B= A- I

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Q: For which value of k does the matrix 4 k A have one real eigenvalue of multiplicity 2?

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