Eigenvalues and Eigenvectors of Matrices

Assignment: Finding Eigenvalues and Eigenvectors of Matrices Instructions: For each matrix given below, calculate the eigenvalues and their corresponding eigenvectors. Provide your detailed solution showing all necessary steps. 1. Given the matrix A = [[2, 1], [1, 2]], find the eigenvalues and eigenvectors. 2. Compute the eigenvalues and eigenvectors for matrix B = [[4, 0], [0, 1]]. 3. For the matrix C = [[0, 1], [-2, -3]], determine its eigenvalues and eigenvectors. 4. Matrix D = [[6, 2], [2, 3]]: Find its eigenvalues and eigenvectors. 5. Compute the eigenvalues and eigenvectors of matrix E = [[3, -1], [0, 2]]. 6. Given matrix F = [[5, 4], [1, -2]], find its eigenvalues and eigenvectors. 7. Matrix G = [[2, 0, 0], [0, 3, 4], [0, 0, 1]]: Find the eigenvalues and eigenvectors. 8. Compute the eigenvalues and eigenvectors for matrix H = [[4, 1, 1], [1, 3, 0], [1, 0, 2]]. 9. Find the eigenvalues and eigenvectors of matrix I = [[7, 5, 2], [1, 4, 3], [2, 1, 8]]. 10. Matrix J = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]: Determine its eigenvalues and eigenvectors.