OC userin Statistics·10 Jun 20182. Let A= 3 S 03 [it] BE where s and t are real numbers. [ 0 -2] Which one of the following statements is true ? (A) A is diagonalizable for all s, and B is diagonalizable only if t = 0. (B) A is diagonalizable if s= 0, and B is not diagonalizable if t +0. (C) A is not diagonalizable if s 70, and B is diagonalizable for all t. (D) A and B are both diagonalizable for all s and all t. (E) A and B are diagonalizable only if s= 0 and t = 0.
OC userin Statistics·7 Jun 2018(0 1 0 5. (9pts) Let P=1 0 11 (a) Calculate PPT 0 0 0 1 -1 0 0 0 -1 0 0 0
OC userin Statistics·3 Jun 2018(2) Find the vertical and horizontal asymptotes of the function f(x) = V3x2 + 2 . Justify your answer. Answer:
OC userin Statistics·3 Jun 20184. BRIEF SOLUTIONS [3 MARKS EACH Evaluate each of the following, and always simplify your answers as much as possible. (a) The interval(s) where the graph of f(x) = ln(1+x2) is concave downward is/are ANSWER ONLY
OC userin Statistics·31 May 20185. (15 marks) Let f(x) = (In x)2. (b) Find all vertical and horizontal asymptotes of f (if any).
OC userin Statistics·28 May 20183. Consider the function f(x) = 12 - Vx| (a) [2 marks] State the domain of f(x)
OC userin Statistics·26 May 20188. Suppose that A is a 2 x 2 matrix which has trace -1 and determinant -6. Its eigenvalues are (A) -1 and -6, (B) 2 and -3, (C) -2 and 3, (D) 1 and 6.
OC userin Statistics·28 May 2018100 000 (c) Are the columns of A linearly independent ? Justify your answer.
OC userin Statistics·22 May 2018PART B - "Show Your Work" Questions - Each correct answer is worth 10 points. (1) Find the equations of both lines through the point (-3,2) that are tangent to the parabola given by y = x2 + x.
OC userin Statistics·19 May 20187. Consider the following system of equations, depending on the parameter k (k + 2)x1 + 8ri + x2 (k + 4).x2 = - 3k +3 12 Which of the following is true? (A) The system is consistent if and only if k -6. B) The system has unique solution if and only if k +0. C) The system has no solution if k = 1. D) The system has infinitely many solutions if and only if k = -6. E) None of the above.
OC userin Statistics·21 May 2018(2) A function f(x) is defined for all positive real numbers and satisfies the equation f(x*) = x3 for every 1 >0. Find f'(16).