OC userin Statistics·20 May 20181. Suppose that A is a 3 x 4 matrix B is a 4x6 matrix, C is a 4x3 matrix and D is a 3 x 6 matrix. Consider the following: (1)(C+AT), (2) DDTC, (3) DBT(C-24"), (4) (AB-D)B",(5) (A" +3C)D (6) ACTDT-2C. Which of the following is true? (a) All six of these are defined. (b) None of these six are defined. (c) (1), (2), (3), (4) and (5) are defined; (6) is not. (d) (1), (3) and (4) are defined; (2), (5) and (6) are not defined. (e) None of the above
OC userin Statistics·19 May 201810. Which of the following is a one-dimensional subspace of R3? A) {(2, y, z)?|x2 – y + 2z=0}. B) {(x,y, 2)7|x + 24 +32 =0}. C) The solution set of Av = 0 where A= 1 -2 3 -1 4 0 0 2 3 D) {(x, y, z)?|x + 2y + 32 = 4}. E) The solution set of Av = 0 where A= 1 0 2 0 2 0 11 0 5
OC userin Statistics·17 May 2018101 21. Let f(x) = sin(x). The largest interval containing x = - on which f is concave up is : (a) (-147, -137], (b) [0,00), (c) (–167, -147), (d) (–157, —137], (e) (–157, – 147). 2 - 4
OC userin Statistics·15 May 201811. (9pts) (a) Suppose that the matrix P = (AB)TCD exists and is 4 x 4. Assuming that A is 3 x 5, B has 5 rows, and D has 2 rows, find the size of A, B, C, D.
OC userin Statistics·12 May 20181. Suppose that 4 and -1 are the only eigenvalues of a 2 x 2 matrix A. Which one of the following statements is true? A) 41 - A is invertible, and there is a nontrivial solution to Av = -v. B) 41 - A is not invertible, and there is a nontrivial solution to Av = v. C) det(41+ A) = det(-I + A) = 0. (D) det(41 - A) = 0 and rank(A + 1) = 1. E) None of the above.
OC userin Statistics·10 May 2018X . Then the linear system AX = B has: -1 a la 11. Let A= Ia a-2 J [ 22 (A) a unique solution if and only if a +-2. (B) a unique solution if and only if a + 1. (C) more than one solution if a = -2. (D) no solution if a = 2. (E) more than one solution if a = 1. (As usual, only one of the above statements is true!)
OC userin Statistics·9 May 2018].x = 23 ), and b = [ ]. Then the 1 2-21 6. Let A = 1 system of linear equations Ax=b (a) has a unique solution if and only a -1. (b) has no solutions if and only if a=3. (c) has infinitely many solutions if and only if a = 1 (d) has a unique solution for every value of a. (e) None of the above
OC userin Statistics·7 May 20184.2 9. The normal to the curve y = 1 at (1, 2) passes through the point (a) (-2, 6), (b) (-7,8), (c) (0,4), (d) (4, -1), (e) (-6,10).
OC userin Statistics·5 May 2018(6) Find an equation of the tangent line to the curve 23-ray + 4y = 8 at the point (2,1).
OC userin Statistics·4 May 2018= -I where I is the 3 x 3 identity matrix. What is 8. For a 3 x 3 matrix A, suppose that A (A - 1)-1? (A) A2 - A+I (B) A-I is not invertible (©) =£(1° ++1) (D) }(42 - A+1) (E)
OC userin Statistics·3 May 2018211 212 213 (3011 +231 3012 + 232 3a 13 + 233 3. If det | 221 222 223 ) = 6, then deta21 +011 222 +212 223 +013 231 232 233/ 231 + 2011 232 + 2012 033 + 2013/ ((A) 6 (B) - 6 (C) – 12 (D) 18 (E) None of the above.