Suppose that E is a 4 x 4 matrix in which every row sums to the constant k. Explain why u = [1,1,1,1]" is an eigenvector of E, and give the corresponding eigenvalue.

Q: and find the corresponding eigenvector.

A: λ is an eigen value if we have Av=λv for some v non-zero.v is called eigen vector.

Q: Suppose that a 5 x 5 matrix A has eigenvalues > −3,-, 1,2,4. Compute det(A). ==

A: Suppose that a 5×5 matrix A has eigenvalues λ=-3, 12, 1, 2, 4. To compute detA.

Q: Let A be a 2 x 2 matrix with real coefficients and eigenvalues A1 = 3, and A2 = 5, which has…

A: Proceed as shown

Q: Suppose that x is an eigenvector of a matrix A with corresponding eigenvalue 6. Then x is an…

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Q: Determine the eigenvector associated with = 3 for the matrix h 6 2-2 25 0 - 2 0 7

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Q: Suppose ?<0λ<0 and ?u are a pair of eigenvalue and eigenvector of a 2×22×2 matrix ?A and ?=??v=Au.…

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Q: Suppose the eigenvalues of A in R²x2 are Â₁ = 1 and Â₂ = 2. What are the eigenvalues of A+ I, where…

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Q: Let A be an n × n matrix and let B = A − αI for some scalar α. How do the eigenvalues of A and B…

A: To check that (eigenvalue of A- alpha) is an eigenvalue of B.

Q: Determine the eigenvalues and as many linearly independent eigenvectors as you can of the matrix A 3…

A: Given that are linear mappings such that We have to prove that  .For this let .so we have As  is…

Q: Show that the eigenvalues of the symmetric matrix 10-4] A = 05 4 -4 4 3 are 9, 3 and -3. Obtain the…

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Q: Let. A be an eigenvalue of an n x n matrix A. Show that. 1² -3 is an eigenvalue of 31

A: Given :  λ is an eigen value of an n×nmatrix  A . We have to prove that  λ2-3 is an eigen value of…

Q: Suppose that A is a matrix such that A2=0. Show that every eigenvalue of A is equal to 0.

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

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Q: Suppose that A and B are square matrices, and that AB = BA. Suppose that v is an eigenvector of A…

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Q: If v is an eigenvector of the matrix A with eigenvalue 2 then 4v is an eigenvector of A with…

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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: Suppose A is a real symmetric matrix whose eigenvalues are A₁ = 1, A2 3, and X3 ei = Find A. A = = 9…

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Q: Suppose that the trace of a 2 x 2 matrix A is tr(A) = -14, and the determinant is det(A) smaller…

A: Let A be a square matrix,  then The trace of A is the sum of eigenvalues and The determinant of A is…

Q: uppose A is a diagonali= . Would this be true if

A: Given, A is a diagonalizable n x n matrix whose eigenvalues are all 1 or -1.