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MATH211 Midterm: MATH211F2012PracticeMidterm1.pdf

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MATH 211
Claude Laflamme

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Faculty of Science Department of Mathematics & Statistics MATH 211 { LINEAR METHODS I { FALL 2012 MIDTERM 1 Exam version: Practice COURSE INFORMATION AND STUDENT IDENTIFICATION INSTRUCTOR SECTION LAB STUDENT I.D. FIRST LAST NAME NUMBER NUMBER NUMBER NAME NAME EXAMINATION RULES 1. No Calculators, electronic equipment, or paper material other than this examination and scantron sheet allowed. 2. Use the back of the previous page for rough work or calculations. 3. Students arriving late will not normally be admitted after one-half hour of the examination time has passed. 4. No candidate will be permitted to leave the examination room until one hour has elapsed after the opening of the examination. 5. All enquiries and requests must be addressed to supervisors only. 6. Candidates are strictly cautioned against: (a) speaking to other candidates or communicating with them under any circumstances whatsoever; (b) bringing into the examination room any textbook, notebook or memoranda not authorized by the examiner; (c) making use of calculators and/or portable computing machines not authorized by the instructor; (d) leaving answer papers exposed to view; (e) attempting to read other students’ examination papers. The penalty for violation of these rules is suspension or expulsion or such other penalty as may be determined. 7. Discarded matter is to be struck out and not removed by mutilation of the examination answer book. 8. Candidates are cautioned against writing in their answer books any matter extraneous to the actual answering of the question set. 9. A candidate must report to a supervisor before leaving the examination room. 10. Answer books must be handed to the supervisor-in-charge promptly when the signal is given. Failure to comply with this regulation will be cause for rejection of an answer paper. MATH 211 ALL SECTIONS - MIDTERM 1 Fall 2012 Part A: Mark your answers on the scantron sheet provided. Exam version: Practice Each question is worth 2 points. 1. What can you say about the general solution of the following system: x + 2y + 3z + 4w = 5 2x + 4y + 6z + 8w = 11 (a) It has no solution. (b) It has one solution. (c) It has three solutions. (d) It has infinitely many solutions. (e) None of the above. 2. What can you say about the general solution of the following system: 2x 1 + 3x 2 − 4x 3 + 6x =40 2x + 3x − 5x + 6x = 0 1 2 3 4 2x 1 + 3x 2 − 4x 3 + 7x =40 (a) It has no solution. (b) It has one solution. (c) The general solution involves one parameter. (d) The general solution involves two parameter. (e) None of the above. 3. Which of the following options constitute the general solution of the following system of linear equations: x − y − z = 0 x + y + z = 4 (a) x = 3, y = 2, z = 1 (b) x = 2, y = 1, z = 1 (c) x = 2, y = 2 − s, z = s (d) x = 2, y = 2 + s, z = s (e) None of the above. Page 2 MATH 211 ALL SECTIONS - MIDTERM 1 Fall 2012 Exam version: Practice 4. Express the general solution of the following system as a linear combination of basic solutions. x1 + 2x 2 + 4x 3 + x 4 0 x1 + 2x 2 + 5x 3 + 2x =40 T (a) s [−2 1 0 0] . (b) t [1 1 − 1 1] . (c) s [−2 1 0 0] + t [3 0 − 1 1] . (d) s [−2 1 0 0] + t [4 − 1 0 0] . (e) None of the above. 5. Find the rank of the following matrix:   1 −2 1   2 −4 2 −3 6 2 (a) The rank is 0. (b) The rank is 1. (c) The rank is 2. (d) The rank is 3. (e) None of the above. 6. The rank of the augmented matrix of the following system of linear equations x + 2y + 3z = 0 x + 2y + 3z = 5 is: (a) 0 (b) 1 (c) 2 (d) 3 (e) None of the above. Page 3 MATH 211 ALL SECTIONS - MIDTERM 1 Fall 2012 Exam version: Practice 7. Consider an homogeneous system of m linear equations in n variables. If the rank of its augmented matrix is r, then the general solution involves: (a) r parameters. (b) m − r parameters. (c) n − r parameters. (d) n parameters. (e) None of the above. 2 −1 8. Consider the matrix transformations S and T induced respectively by the matrices A = 1 2 −1 3 and B = Then S ◦ T is: 1 2 (a) not a matrix transformation. (b) a matrix transformation induced by the matrix1 3
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