13 is diagonalizable. Its eigenvectors are: The matrix A = 42 3. 4 3. 4 3.

For matrix A, find the associated eigenvalues. A = [] O2 and 3 O3 and 5 O1 and 5 5 and -1

Let B be a 2 × 2 matrix such that 7B²5B+3I = 0. Is B invertible? It so, what are the eigenvalues of B-¹? Justify your answer.

Let A = 3 1 2 4 Find the eigenvalues and the corresponding eigenvectors of matrix A ck that it is diagonalizable by computing AP and PD.

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

Let A be a symmetric n x n matrix. Let A1 and A2 be two eigenvalues with eigenvectors vị and v2 for A, respectively. Show that vi and v2 are orthogonal.

Let M be a 2 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo = 5 3 V₁ = V2 = 2 xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C₂ V₂ = In general, xk= V1+ V2 ) * vi+ k ) v2 Specifically, x4 = For large k, xk≈ k

Find the eigenvectors of the matrix A= 1 1 -1 0 5 0 0 1 -1

Consider the matrix 2 -4 A = (-²₁ 2¹) -1 (a) Compute the eigenvalues and the corresponding eigenvectors. (b) Let v = = [2, 1], compute A10¹0000 V.

Q3: Compute the eigen values and eigen vectors of the following matrix 10 1 1 0 0 3 1 04: