Plz solve all

19. Find the matrix A if ( 2 \]) - [ 81' (a) -10 3 3 (e) 4 13 20. Find the reciprocal of 5 (i.e., 5-1) modulo 14. (a) 7 (b) 10 (c) 2 (d) 3 (e) 5 21. Suppose that A is a matrix with eigenvalues A = 9 and A = 8, with corresponding eigenvectors and , respectively. Find azz, i.e., find the entry in row 2, column 2 of the matrix A. (a) 4 (b) 5 (c) 1 (d) 3 (e) 2 22. Fred the giraffe is either happy or sad. If he is happy one day, then he is happy the next day four times out of five. If he is sad one day, then he is sad the next day one time out of three. Over the long term, what are the chances that Fred is happy on any given day? (a) ; (b) is (c) 19 (d) . (e) To 23. Let A be an n x n matrix. Which of the following statements is NOT equivalent to the rest of the statements? (a) The reduced row echelon form of A is In (b) A is invertible (c) Ax = 0 has infinitely many solutions (d) det(A) # 0 (e) A is expressible as a product of elementary matrices 24. For what value of a does the following system have no solution? X1 + 212 + 4x3 = 1 201 + 12 = 3 4x1 + 512 + 8.3 = 5 a12 + 8x3 = -2 (a) -3 (b) -2 (c) 1 (d) 2 (e) 3