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import numpy as np

def determinant(matrix):
  """Calculates the determinant of a 3x3 matrix."""
  a = matrix[0][0]
  b = matrix[0][1]
  c = matrix[0][2]
  d = matrix[1][0]
  e = matrix[1][1]
  f = matrix[1][2]
  g = matrix[2][0]
  h = matrix[2][1]
  i = matrix[2][2]

  return a * (e * i - f * h) - b * (d * i - f * g) + c * (d * h - e * g)

def matrix_subtraction(matrix1, matrix2):
  """Subtracts two matrices."""
  result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
  for i in range(len(matrix1)):
    for j in range(len(matrix1[0])):
      result[i][j] = matrix1[i][j] - matrix2[i][j]
  return result


def matrix_multiplication(matrix1, matrix2):
  """Multiplies two matrices."""
  result = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
  for i in range(len(matrix1)):
    for j in range(len(matrix2[0])):
      for k in range(len(matrix2)):
        result[i][j] += matrix1[i][k] * matrix2[k][j]
  return result


def find_eigenvalues_and_eigenvectors(matrix):
  """Finds eigenvalues and eigenvectors of a 3x3 matrix."""
  identity_matrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
  eigenvalues = []
  eigenvectors = []
  for lambda_val in range(-10, 11):  # Search for eigenvalues within a range
    new_matrix = matrix_subtraction(matrix, [[lambda_val, 0, 0], [0, lambda_val, 0], [0, 0, lambda_val]])
    if abs(determinant(new_matrix)) < 1e-6:  # Check for near-zero determinant
      eigenvalues.append(lambda_val)
      # Find eigenvector corresponding to the eigenvalue
      # Solve the system of linear equations (A - λI)v = 0
      # Example: using Gaussian elimination or other methods
      # Here we are just finding a non-zero solution
      eigenvector = [0, 0, 0]
      for i in range(3):
        if abs(new_matrix[0][i])> 1e-6:
          eigenvector = [1, 0, 0]
          break
        if abs(new_matrix[1][i])> 1e-6:
          eigenvector = [0, 1, 0]
          break
        if abs(new_matrix[2][i])> 1e-6:
          eigenvector = [0, 0, 1]
          break


      eigenvectors.append(eigenvector)
  return eigenvalues, eigenvectors


# Example usage:
matrix = [[2, 1, 0], [0, 2, 0], [0, 0, 3]]
eigenvalues, eigenvectors = find_eigenvalues_and_eigenvectors(matrix)
print("Eigenvalues:", eigenvalues)
print("Eigenvectors:", eigenvectors)