Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 21 = 5, x, = (1, 2, -1) 12 = -3, x, = (-2, 1 0) o] A3 = -3, x, = (3, 0, 1) -2 2 -3 A = 1 -6 -1 -2 %3D -2 2 -3 1 Ах, — 1 -6 = 1,×1 %3D 2 -1 -2 -2 2 -3 Ax2= 2 1 -6 -1 -2 -2 2-3 3. Ax3 2 1-6 0. -1 -2 0.

Q: 3. Let A € Mn,n and let λ be an eigenvalue of A. Suppose A satisfies the equation 2A²+5A-10In Show…

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Q: Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. -4-2 2₁-11, x₁ =…

A: Given matrix is A = -4-23-2-7612-6

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: Find matrices D and P of an orthogonal diagonalization of A. (A graphing calculator is recommended.…

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Q: log2(9-m) = log23m How do you solve this log problem using the one to one property?

A: To solve the given logarithmic equation

Q: Verify that A, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 8, x (1, 0, 0)…

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Q: Exercise: Let A be an invertible n x n matrix. Suppose that u ER" is an eigenvector of A with…

A: For λ=2, u∈ℝn is an eigen vector of the matrix A and for λ=-7, v∈ℝn  is an eigen vector of A Note:…

Q: 2 -1 -1 4 -1 1 2 = 1 -1 0 -1 -1 - 0 −1 1 30 020 03 10 0 ㅜㅜㅜ -1 -1 -1 -1 0

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Q: 2 1 -1 -1 4 -1 1 2 = 1 -1 0 -1 1 -1 0 -1 1 300 0 -1 -1 020 -1 −1 −1 003 -1 -1 0

A: if a matrix A is diagonalized it can be written as  A=PDP-1 where D is the diagonal matrix formed by…