Find a 2x2 matrix A that has eigvalue λ = 3 with associated eigenvector eigenvalue X = 2 with associated eigenvector A X 1 2 2 H. 5 and [3] 5

The matrix A := C = 12 -2 -3 13 has an eigenvector 6 (8) with eigenvalue 10. What is c?

1 Let P = -2 - Find p P. Deduce P, if it exists, from the result of -1 p' P. You can also calculate P 1 using the traditional approach but this will be slower. 2. Let A be a 3 x 3 matrix with the following eigen-pairs: 1 (1, ):(1, 0 ):G -2 ).

Find the eigenvalues A1 < A2 < Ag and associated unit eigenvectors ū1, ü2, ūz of the symmetric matrix 4 -2 -27 A -3 5 -2 -3 The eigenvalue A -8 has associated unit eigenvector ủ1 = The eigenvalue A2 = 0 has associated unit eigenvector u2 =

Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2 = -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V2 Consider the difference equation with initial condition xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, X = Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk A V2 7)k V₂

Matrix A has the eigenvalue 2 = 5 and eigenvector v. Find generalized eigenvector. 7 1 01 1|,λ5, ν = A = -3 4 -2 1 41 X2=

Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors ủ1, ủ2, ūz of the symmetric matrix 4 -2 -2] A = -2 -2 4 -2 4 -2 The eigenvalue A1 -6 has associated unit eigenvector ủ1 = The eigenvalue X2 = 0 2 has associated unit eigenvector u2 ||