(i) For which values of k does A have two distinct real eigenvalues? Explain. ii) When is there no real eigenvalues? Explain

Q: Verify that λ, is an eigenvalue 8 -1 3 0 6 1 07 0 Ax₁ = Ax₂ = A 8-1 3 0 61 0 0 07 0 8-13 0 0 6 1 2…

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Q: 1 If A = has eigenvalues =2 and A =-2, then z= Number

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Q: pls explain to me step by step. thanks

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Q: Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to…

A: As per the question we have to explain what happens in the relationship (dynamic system) as time…

Q: - a) Let A = 1 1 01 -1 1 Find AT A.

A: We solve only (a).( According to guidelines)

Q: Suppose that A= det A-XI4 = 0. 42 0 4 02 -1 0 0033 04 0 7 . Find the eigenvalues of A, i.e. the A…

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Q: Let x e gl(n, F) nave n distinct eigenvalues a,,..., an in F. Prove that the eigenvalues of ad x are…

A: Let B be a basis of in which x is diagonalizable. Let A be the matrix with respect to this basis.…

Q: i) Find the Eigenvalues of A = 3 5 et d = 3 in the above matrix A, compute the Eigenvalues and…

A: Let us consider a matrix A of order n x n then the eigen values  and eigen vectors  are obtained as…

Q: If = and t = are eigenvectors of a matrix A corresponding to the eigenvalues A1 = 1 and Az = 3,…

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Q: the matrix -2 -3

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Q: Are linearly independent? Justify your answer.

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Q: The matrix A = has one eigenvalue of multiplicity 2. Find this eigenvalue and the dimension of its…

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Q: (d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.

A: TrueJustification:Suppose v is an eigenvector for a matrix A and a matrix B.Then there exist real…