OC userin Statistics·11 Apr 201811 • -2 D a la-1 8. Let A = 1 la-9- 94 The linear system AX = B has: (A) more than one solution if and only if |al 3. (B) a unique solution if and only if |al + -3. (C more than one solution if a = -3. ((D) ho solution if a = 3. (E)None of the above. (Exactly one of the above statements is true.)
OC userin Statistics·9 Apr 2018Part II: Answer in the space provided below each question. Continue on the facing page (i.e. back of the previous page). After that, use one of the continuation pages at the end of this booklet, being sure to indicate its location. II.1 (10 points) (a) Find the distance from the point P(2,1,0) to the line L determined by the two points A(1,1,1) and B(2,-1,3).
OC userin Statistics·5 Apr 20189. How many critical numbers does the function f(x) = x2+2x-3 have on the interval [ -2,2]? (a) 4 (b) o (c) 1 (d) 2 (e) 3
OC userin Statistics·6 Apr 20184. Consider the function f(x) = 4x2 – 22 - 1 (b) [2 marks] On what part of the real numbers is f(u) continuous?
OC userin Statistics·4 Apr 201810. (8pts) (a) Find the value(s) of k for which ū = 0 , y = k 4 and w = are linearly 1 \k/ independent in R3.
OC userin Statistics·1 Apr 2018(b) Suppose that the linear transformation T: R2 R2 has eigenvalues X = 2 and = 3, with 1 ] corresponding eigenvectors 1, respectively. Find the standard matrix of T. and
OC userin Statistics·24 Mar 20187. Consider the following system of equations, depending on the parameter k (k +2.11 + 8.rı + x2 = (k + 4).x2 = 3k + 3 12 Which of the following is true? A) The system has no solution if k = 1. B) The system has infinitely many solutions if and only if k = -6. C) The system is consistent if and only if k + -6. D) The system has unique solution if and only if k +0. E) None of the above.
OC userin Statistics·23 Mar 20189. If S: R2 + R2 is the orthogonal projection onto the line 6x + 2y = 0, which of the following is a pair of eigenvectors of S ? -1] [6] [ 2 ] [-2] [ -6] ([:'],[] [ 3 ] [-1 (a) [?], [=] m[7] [8] m[); [3] (a) []["] 1 [ - J' [ 2 29 ]
OC userin Statistics·20 Mar 2018J . 15. Among the matrices A= 0 0 0 1 0 0 1 0 0100 | 1 0 0 0 B= /0 0 1 0 1 0 100) 1 -1 0 ,C=1 0 1 3 0 0 0 1 ) / 0 1 0 /1 0 0 | 1 1 0 D= 200, E= 10-20, F01 0. 100 1 ) 0 0 1 0 0 1 A) A, B, C, E and F are elementary, the others are not; B) B, E and F are elementary, the others are not; C) A, B, E and F are elementary, the others are not; D) none of these matrices is elementary, E) they are all elementary.