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Q: What is the relationship between the characteristic polynomial and the eigenvalues of A?

A: Here. We have to find the relationship between eigenvalues and characteristics polynomial.

Q: Let 1 be an eigenvalue of the n x n matrix A. Let B = A- AI. Show that B is not an invertible…

A: Let A be an n×n matrix. The characteristic polynomial of A is the function f(λ) given by…

Q: Determine the geometric multiplicity and the algebraic multiplicity of the eigenvalues of the matrix…

A: Given            The characteristic equation of A is…

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: 7. Consider Pauli matrices: 1 and o, 1 0 i and find their eigenvalues and eigenvectors. Finally,…

A:

Q: Let A be a diagonalisable n x n matrix with eigenvalues A1, 2, · · , An Prove that det(A) did2 · . ·…

A: Diagonalisable matrix: A n×n matrix A is said to be diagonalisable if there exist a non-singular…

Q: Find the eigenvalues and associated eigenvectors of the matrix [2 -2 1 -5].

A: The given matrix is: 2-21-5 To Find: The eigenvalues and associated eigenvectors.

Q: Choose the 2 by 2 nondiagonal matrix such that its eigenvalues are different positive numbers…

A: We first write a 2×2 non diagonal matrix whose eigen values are different positive numbers then we…

Q: A is a matrix with eigenvector 51-31- || 1 of eigenvalue -1 and eigenvector of eigenvalue -2. What…

A: The given problem is to find the matrix A with the given eigenvectors corresponding to the given…