Question 2 (Eigenvalue method) Question 2. Find the general solution of the homogeneous linear system below using the eigenvalue method. - (2) y
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- Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.Find an orthonormal basis for the solution space of the homogeneous system of linear equations. x+yz+w=02xy+z+2w=0
- For the linear system x' = Find the eigenvalues and eigenvectors for the coefficient matrix. λι ×₁ = 0,0₁ = and X2 = [8] [8] help (numbers) help (matrices) help (numbers) help (matrices) Book: Section 3.4 of Notes on Diffy QsUse a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction -Integration11) Find the values of such that the equations have non-trivial solutions. What are the eigenvalues and eigenvectors? (6-2) x + 3y = 0 3x - (2+2)y = 0
- Let 1 A = -2 1 Consider the system of equations = A. (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system. %3D (c) Determine whether 7 Ở is a node, or a saddle, or a spiral point. (d) Determine the stability of 7 = 0. 2.(1 point) Suppose A is a 2 x 2 real matrix with an eigenvalue X = 5 + 3i and corresponding eigenvector Determine a fundamental set (i.e., linearly independent set) of solutions for y Enter your solutions below. Use t as the independent variable in your answers. (t) v = (t) = -1+ i Ay, where the fundamental set consists entirely of real solutions.Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion2.
