Question 8: [45 marks] -1 5 -1 For the given matrix A= 0 O 7 (a) Find all eigenvalues and present them in the ascending order. [25 marks] (b) Which of two given vectors vi and v2 is the eigenvector of the matrix A, where vil = (1, 0, 4) and v2 = (1, 0, - 4)? What is the corresponding eigenvalue? [20 marks] Rubric: 2 marks if the matrix A - // has been calculated correctly; 5 marks if the determinant |A - )/ | has been developed correctly; 2 marks if one of the roots has been guessed correctly; 8 marks if the quadratic polynomial has been found correctly by either method; 6 marks if other two roots have been found correctly; 2 marks if the eigenvalues are presented in the ascending order correctly. Rubric: 5 marks if the product Avi has been calculated correctly; 3 marks if it was correctly determined that vector vi is not an eigenvector of matrix A; 5 marks if the product Av2 has been calculated correctly; 3 marks if it was correctly determined that vector v2 is the eigenvector of matrix A; 4 marks if the eigenvalue corresponding to vector v2 was determined correctly