Problem #18: Let [2 marks] 7 12 24 A = 0 1 0 0 0 1 Find a basis for the eigenspace corresponding to A = l. 2 5 3 4 2 5 3 4 3 4 2 5 (A)1,0(B)1,0(C)1,0(D)1,0(E)1,0(F)1,0 0 1 o 1 0 1 o 1 o 1 o 1 2 4 2 4 (G) 1 , 0 (H) 1, 0 0 1 0 1 Problem #13: Pr0blem # 19: Which of the following statements are always true? [2 marks] (1) Suppose that the characteristic polynomial of a matrix A is (/l - 3)7(A - 5)6. Then the determinant of A is nonzero. (ii) Every 179 X 179 upper triangular matrix has 179 distinct eigenvalues. (iii) Suppose that A = 5 is an eigenvalue of a matrix A. Then the equation Ax = 5x has innitely many solutions. (A) (iii) only (B) (i) only (C) (ii) only (D) all of them (E) (ii) and (iii) only (F) (i) and (ii) only (G) none of them (H) (i) and (iii) only Problem #19