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
- Consider the linear system = Find the eigenvalues and eigenvectors for the coefficient matrix. λι and = V₁ = 12 = ປີ2 = [8] [8] help (numbers) help (matrices) help (numbers) help (matrices) Find the real-valued solution to the initial value problem x = -3x1 - 2x2, x = 5x1 + 3x2, x1(0) = 7, x2(0) = −10. Use t as the independent variable in your answers. x1(t) help (formulas) x2(t) = help (formulas) Book: Section 3.4 of Notes on Diffy QsSOLVE CAREFULLY!! Please Write Clearly and Box the final Answer(s) Label them ( C& D)Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction -Integration
- 11) 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(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.
- Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.Solve pleaseConsider the initial value problem Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 72 for the coefficient matrix of this linear system. λ = x₁(t): = x₂(t) = x₂ (t) = help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use c₁ and c₂ to denote arbitrary constants, and enter them as "c1" and "c2". Solve the original initial value problem. x₁(t) = , V₁ = V1 = = , V₂ = help (formulas) help (formulas) help (formulas) x₁ x₂ help (formulas) = = 3x2, x₁ (0) = 2, -3x1 +6x2, x₂(0) = 6.