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- 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 all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.CAPSTONE Explain how to determine whether an nn matrix A is diagonalizable using a similar matrices, b eigenvectors, and c distinct eigenvalues.
- P.nileshQ1 (a) State a suitable numerical method that can be used to determine The largest eigenvalue The smallest eigenvalue (ii)Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction - Integration
- SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer(s) Label them ( C& D)Determine the eigen values and eigen vectors of the system of linear differential equations incowing temperature, pressure and concentrat 4P-4T + C dp dt dT = 4P - T + 3 C dt 6 dc = P + 5T - C dt 61 = 0% (00) Hint A = C 40 noidy 1-4p1 4 (1-4 4T! 3 1 5 -1 po bon enodos 43 P SP-DC 32 SH 0- 4 Sc + Sop DoupsFind the matrix A of the quadratic form associated with the equation. бх2 - 5ху - бу?+8 %3D 0 -5/2 A = -5/2 -6 Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 13 13 2 Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) [[-5, 1],[1, 5]]| × P =
- already found the value of A3 plz find the value of A7 and answer b)?!!!! the value of p = 9 Q5(a) Find the eigenbasis of the matrix and diagonalize it (if possible): [4 p p A = p 10 1 1 6 Use this diagonalization to find A' and A'. (b) For the matrix in part (i), find A' and A using Cayley-Hamilton theorem.Matrix A = (2 x 2) Row 1 is: 3/4 -1/4 row 2 is: -1/4 3/4 (ii) Determine the eigenvalues and eigenvectors of A. (May you please describe in depth (iii) What are the algebraic and geometric multiplicities of each eigenvalue? Is A diagonalizable and if so, what is the diagonalization (i.e., D and P)? (iv) Assume that the above A corresponds to the dynamical system xk = Axk-1 with xk = (2 x 1) row 1 is: 1 Row 2 is: 2 Determine the x10 What is the steady-state of this dynamical system? (May you please describe in depthbased on the image provided. Assisstance please.