OC userin Statistics·2 Jan 20183.(bola) let n = ( ) (1 2 3 3. (8pts) Let A= 2 4 6 14 8 12 (a) Solve the homogeneous system AX = 0. (1)
OC userin Statistics·31 Dec 20173. Let u and v be vectors in R3 such that ||u|| = 2, |v|| = 5, and u.v=3. Then ||u - vll= (A) 35 (B) /43 (C) 43 (D) 23 (E) 29
OC userin Statistics·30 Dec 2017[ ] , V3 = 12. Let V1 = -3 4 -3 -1 , V2 = [-11 -6 , V4 = [ 1] 0 L-1 Which one of the following statements is true ? (A) {V1, V2, V3} is a basis of R3, (9) (v.) bei of span {[:] 7:]} i] [- (B) {V1, V2} is a basis of Span ( 0] [ 0 (C) {V1, V2, V4} is a basis of Span{V1, V2, V3, V4}, (D) {V1, V2, V3} is a basis of Span{V1, V2, V3}, (E) {V1, V2} is a basis of Span{V3, V4}.
OC userin Statistics·27 Dec 2017(4) Find the equations of both lines through the point (2, -1) that are tangent to the parabola given by y= 22 +2.. a tenere et bien
OC userin Statistics·27 Dec 2017a. The plane has de estar contre : 1-6-6-li) mesur paper [7] 9 [ 2 3 6. The plane 7 has the vector equation 1 = + 2 + . A vector perpen- dicular to this plane is (A) (1, -1,27 (B) (1,-1,1]? (C) (7,9,117 (D) (1,0,–2,7 (E) (-1,7, -9]T
OC userin Statistics·29 Dec 20171. If A = ( ) has determinant -3, B =( le d ) lcd has determinant 2, 20 20 and C=1 ), then the determinant of 3adi (C-1) is la-2a 6 -- 26 ): the B) -12. C) - D) - (E) None of the above. 10 Wien
OC userin Statistics·26 Dec 20173. (10 marks) A camera is located 10 meters to the west from a straight north-south road along which a car is traveling to the south at a speed of 20 meters per second. The camera turns so that it is pointed at the car at all times. How fast, in radians per second, is the camera turning as the car passes closest to the camera?
OC userin Statistics·24 Dec 20172. (10pts) Suppose A is a 3 x 3 matrix such that det A=2. Find det B in each of the following cases: (a) B= -A(AT)A-1
OC userin Statistics·23 Dec 20173. Consider the function f(x) = 12 - Vx| (c) [3 marks] Using your answer in part (b), show that f(x) is continuous on its domain. Justify your answer.
OC userin Statistics·20 Dec 20179. (8pts) Consider the linear transformation T:R2 R3 defined by (x + 4y -C 3y and the linear transformation U: R3 ©)-(3) •©–0). ()-(6), «()-(-) R2 such that (a) Find the matrices of T and U.
OC userin Statistics·15 Dec 20177. Suppose that 4 and -2 are the only eigenvalues of the matrix A. Which of the following statements is true? (a) 41-A is invertible, and there is a nontrivial solution to Av = -2v. (b) det (41+ A) = det(21 - A) = 0. (c) 41 - A is not invertible, and there is a nontrivial solution to Av = -2v. (d) det(41+ A) = 0, and there is a nontrivial solution to (21 - A)v = 0. (e) none of the above
OC userin Statistics·16 Dec 201717. Let f(x) = * - 9x2 - 273.x - 2. The function f has a point of inflection at x = (a) -1, (b), (c) 4, (d) 10, (e) 13.
OC userin Statistics·16 Dec 2017(b) Where the system has infinitely many solutions, write these in parametric form.
OC userin Statistics·15 Dec 20171. (10 marks) Determine the following limits: (a) lim ( x2 - 4x +3 - x2 +1) tan-x (6) lim x=0 secx - 1