Suppose A E M₂ (R) is not a multiple and consider the linear function L on M₂ (R) with the criterion L (X) = AX - XA. Obtain eigenvalues and eigenvectors of L.
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- q4VII. Run two iterations using normalized power iteration method for the following matrix and initial vector. Roughly predict the dominate eigenvalue and corresponding eigenvector. A = [ ²₁ 2] ₁ x₁ = 1 []Let x(t) x₁ (t) x' (t) x₁ (t): = = If x (0) = x₂(t): = = = ] Put the eigenvalues in ascending order when you enter x₁ (t), x₂(t) below. exp( t) + exp( x₁(t) x₂(t) -27 x₁(t) + 12x₂(t) -56 x₁(t) + 25 x₂(t) 4 be a solution to the system of differential equations: -2 exp( find x(t). t) + exp( t) t)
- Given that the matrix A has eigenvaluesX₁ = -5 with corresponding eigenvector ₁ = and A₂ = 3 with corresponding eigenvector 2 = A = 1 [:] , find A. [:]Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. 2₁9, x₁ (1, 0) = - [8. AX1 = AX2 A = = 9 0 0-9 = 22-9, x₂ = (0, 1) = = ↓ 1 = 9 0 -9 22x2 ~-(:D)- E= -0)-*-*2 1 0-9 ↓1 •[:] · = 2₁x1Suppose that B ∈ M 6(R), and that pB(t) has at least 5 real roots. How many non-real eigenvalues does B have?
- 7. Let the 2 x 2 matrix A have real, distinct eigenvalues and μ. Suppose that an eigenvector of A is (1,0)" and an eigenvector of u is (-1,1)". Sketch the phase portraits of is x = Ax for the following cases: (1) 0 0. وچستان ستان جThe matrix has two distinct eigenvalues with ₁Let A (a) Determine the eigenvalues X₁ and ₂ of A where X₁Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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