Exam 3.pdf - Print Test PRINTABLE VERSION Test 3 You scored...

This preview shows page 1 out of 6 pages.

Unformatted text preview: 12/11/2018 Print Test PRINTABLE VERSION Test 3 You scored 73 out of 74 Question 1 Your answer is CORRECT. The augmented matrix for a system of linear equations is ⎛ 1 4 −3 −2 ⎜ ⎜ 0 1 k + 3 k ⎝ 0 −k −4 −1 ⎞ ⎟. ⎟ Determine the value(s) ⎠ of k for which the system has infinitely many solutions: a) k ≠ 1, k ≠ −4 b) k = 1 c) k = 1, k = −4 d) k = −4 e) k ≠ −1, k ≠ 4 f) None of the above. Question 2 Your answer is CORRECT. Given the matrices −4 −3 A = ( 1 3 −2 ), B = ( 2 −4 a) −7 b) 6 c) −14 d) 2 e) d 3,2 f) None of the above. 2 −3 5 7 2 3 ) , and C = ( 5 3 3 ) , let D = AB − 4C . Find the entry d 3,2 . is not defined 1/6 12/11/2018 Print Test Question 3 Your answer is CORRECT. Let matrix ⎛ 1 A = ⎜ −1 ⎝ 0 a) 9 b) −1 c) −12 d) 7 e) 12 f) None of the above. 0 1 3 4 ⎞ −4 ⎟ . 1 Find the element in the (1, 2) position of −1 A . ⎠ Question 4 Your answer is CORRECT. The determinant of the matrix of coefficients of the system of equations x + 2y − 2z = 3 −2y − 2z = −4 2x + 3y − 2z = −4 is −6. Give the value of z to the solution set. a) 2 b) 4 c) − d) − e) f) 5 3 8 3 14 3 None of the above. Question 5 Your answer is CORRECT. 2/6 12/11/2018 Print Test Given the set of vectors S = {v1 = (0, 1, x), v2 = (x, 0, −3), v3 = (−4, 1, −7), v4 = (1, x, −4)}. The values of x such that the vectors a) x = −3, x = 4 b) No real numbers. c) x = −3, x = −4, x = 1 d) x = 1, x = 4 e) All real numbers f) None of the above. v1 , v2 , v3 , v4 are linearly dependent are: Question 6 Your answer is CORRECT. Given the set of vectors S = {v1 = (0, 1, x), v2 = (x, 0, −4), v3 = (2, 1, −2), v4 = (−1, x, 2)}. The values of x such that the vectors a) x = −4, x = 2 b) x ≠ −4, x ≠ 2 c) x ≠ −4, x ≠ −2 d) x = 4, x = −2 e) x ≠ 4, x ≠ 2 f) None of the above. v1 , v2 , v3 are linearly independent are: Question 7 Your answer is CORRECT. Find the eigenvalues of ⎛ A = ⎜ ⎝ a) −1 3 0 2 0 0⎟. 2 −3 −1 ⎞ ⎠ λ 1 = 2, λ 2 = −3, λ 3 = −1 3/6 12/11/2018 Print Test b) λ 1 = 2, λ 2 = 3, λ 3 = −1 c) λ 1 = 2, λ 2 = 3, λ 3 = 1 d) λ 1 = −2, λ 2 = −3, λ 3 = 1 e) λ 1 = −2, λ 2 = −3, λ 3 = −1 f) None of the above. Question 8 Your answer is CORRECT. The number −3 + 2i is an eigenvalue of a 2 × 2 constant matrix −1 A; v = ( 3 ) + i( 2 ) corresponding eigenvector. A fundabmental set of solutions for the linear differential system 3 a) x1 = e b) x1 = e c) x1 = e d) x1 = e e) x1 = e f) None of the above. −3t [cos(2t) ( −1 ) − sin(2t) ( 0 −3t −1 [cos(2t) ( )] , x2 = e −3t )] , x2 = e −3t −1 3 2 )] , x2 = e −3t −1 )] 2 0 [cos(2t) ( −1 ) + sin(2t) ( )] 2 3 [cos(2t) ( 0 )] 2 ) − sin(2t) ( 3 3 ) − sin(2t) ( −1 ) + sin(2t) ( [cos(2t) ( 3 )] 0 3 [cos(2t) ( −1 ) + sin(2t) ( 0 is: 3 0 0 ) − sin(2t) ( [cos(2t) ( −3t 0 −1 [cos(2t) ( = Ax ) + sin(2t) ( 0 3 2 −3t )] , x2 = ie ) + sin(2t) ( ′ −1 [cos(2t) ( 0 −1 [cos(2t) ( x 2 3 ) − sin(2t) ( 2 −3t −3t 2 2 −3t )] , x2 = ie is a 0 )] 2 Question 9 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 944 Given the system of equations 2x1 − 3x2 + 3x3 + 3x4 = 3 3x1 − 5x2 + 3x3 + 7x4 = 5 x1 − 2x2 + x3 + 3x4 = 0 (a) Write the augmented matrix for the system. (b) Reduce the augmented matrix to row-echelon form. 4/6 12/11/2018 Print Test (c) Give the solution set of the system. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 10 Your answer is CORRECT. This is a written question, worth 10 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1023 Given the matrix −2 −3 3 A = ⎜ −6 −5 6⎟ −6 7 ⎛ ⎝ −6 = −2 is an eigenvalue of A and λ = 1 is an eigenvalue of (a) Find the eigenvector(s) corresponding to λ = −2 . (b) Find the eigenvector(s) corresponding to λ = 1 . (c) Find the general solution of x = Ax. λ1 2 ⎞ ⎠ A of multiplicity 2. 1 2 ′ a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 11 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1123 Let A = ( 6 −2 2 2 (a) Find the eigenvalues of A . (b) Find the eigenvectors of A . (c) Find the general solution of the linear differential system x ′ ) . = Ax a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 12 Your answer is CORRECT. 5/6 12/11/2018 Print Test This is a BONUS question worth 1 point. If the matrix of coefficients of a system of n linear equations in system has no solutions. a) Always true. b) Sometimes true. c) Never true. d) None of the above. n unknowns does not have an inverse, then the Question 13 Your answer is INCORRECT. This is a BONUS question worth 1 point. If a system of n linear equations in n unknowns is inconsistent, then coefficients. a) Always true. b) Sometimes true. c) Never true. d) None of the above. 0 is an eigenvalue of the matrix of 6/6 ...
View Full Document

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture