Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = 5, x₁ = (1, 2, -1) A₂ = -3, x₂ = (-2, 10) A3 = -3, x3 = (3, 0, 1) Ax1 = Ax2= Ax3 = A = -2 -2 -1 -2 -2 -1 -2 2 -3 2 1 -6 -2 2 -3 2 1 -6 0 -1 -2 2 = DE 2 -3 2 1 -6 0 -1 -2 IJ 0 2-3 3 I 2 1 -6 0 = E 5 = -3 N7 2 -1- 3 -3 0 = 2₁x1₁ = 1₂x2 = 13x3

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: Verify that 2; is an eigenvalue of A and that x; is a corresponding eigenvector. = 3, x1 = (1, 0) A…

A: The given matrix is A=300-3 corresponding to this the eigenvalues and the eigenvectors are λ1=3,…

Q: Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 %3D 13, х1 %3…

A: Given A = -14-645-12-2-43λ1 = 13, x1 = (1, 2, -1)λ2 = -3, x2 = (-2, 1, 0)λ3 = -3, x3 = (3, 0, 1)

Q: Verify that λ; is an eigenvalue of A and that X; is a corresponding eigenvector. = λ₁4, x₁ = (1, 0,…

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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:…