MATH 220 NAMEEXAM I STUDENT NUMBERSPRING 2011 INSTRUCTORVERSION A SECTION NUMBEROn your scantron, write and bubble your PSU ID , Section Number, and Test Version. Failureto correctly code these items may result in a loss of 5 points on the exam.On your scantron, bubble letters corresponding to your answers on indicated questions. Itis a good idea for future review to circle your answers in the test booklet.Check that your exam contains 20 multiple-choice questions, numbered sequentially.Answer Questions 1–20 on your scantron.Each question is worth 5 points.THE USE OF A CALCULATOR, CELL PHONE, OR ANYOTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THISEXAMINATION.THE USE OF NOTES OF ANY KIND IS NOT PERMITTEDDURING THIS EXAMINATION.MATH 220 EXAM I, VERSION A PAGE 21. Solve the linear system2x1− x2+ 3x3= −53x1+ 2x2− 6x3= 3−x1+ x2= 6a)−533, −353, −569b)1, 5,23c)−11, −5,23d)⋆−1, 5,232. How many solutions does the following system have?3x1+ 5x2+ 4x3= −12x1− 2x2+ x3= 07x1+ x2+ 6x3= 2a)⋆ Noneb) Onec) Infinitely many, with 1 free variabled) Infinitely many, with 2 free var ia blesMATH 220 EXAM I, VERSION A PAGE 33. According to the graphhow can we best describe the vector w in terms of the vectors u and v?a) 2v + ub) 3v − uc)⋆ 3v + ud) 2v − u4. For which value(s) of h is b =0hin the set spanned by the vectors a1=21anda2=10?a) h = 0b) h = 1c) h = 2d)⋆ h = any real number.MATH 220 EXAM I, VERSION A PAGE 45. Which of the following is a linearly independent set?a)⋆022,043,133b)4230,211.50c) v, 2v + u, 0d)13,23,276. What is the standard matrix for rotation of the xy-plane about the origin by 180◦?a)0 -1-1 0b)-1 00 1c)⋆-1 00 -1d)0 2-2 07. Which of the following matrices is invertible?a)1 32 6b)1 23 45 6c)⋆1 4 72 5 83 6 10d)2 0 13 0 11 0 1MATH 220 EXAM I, VERSION A PAGE 58. Find a basis of the column space Col A for the matrixA =2 3 −2 1 44 5 −3 11 44 6 −4 3 4.a)244,356,−2−3−4b)⋆244,356,1113c)244,356,−2−3−4,1113,444d)244,3569. The following are augmented matrices of corresponding linear systems. Which system isconsistent when b = [b1, b2, b3]Tis any vector in R3?a)1 2 3 b14 5 6 b27 8 9 b3b)1 2 3 b14 5 6 b26 8 10 b3c)0 1 −4 b12 −3 2 b24 −5 0 b3d)⋆1 3 4 b1−4 2 6 b2−3 −2 −7 b3MATH 220 EXAM I, VERSION A PAGE 610. Which of the fo llowing multiplications will g ive you a vector in R4?a)a b cd e fxyzb)a b c de f g hi j k lwxyzc)⋆1 24 56 89 12xyd)0 1 −4 32 −3 2 1wxyz11. Which of the fo llowing is not a linear transformation?a) T (x) = 3xb) Tx1x2=0 1−1 0x1x2c) Tx1x2= x1+ x2d)⋆ Txy= xyMATH 220 EXAM I, VERSION A PAGE 712. Find the entries in the second row of AB where A =2 −5 0−1 3 −46 −8 −7−3 0 9and B =4 −67 13 2.a)⋆ [5, 1]b) [5, −1]c) [2, 3]d) [2, −3]13. Which of following matrices is in reduced echelon f orm?a)1 0 0 00 1 1 00 1 0 10 0 0 0b)1 0 0 00 1 1 00 0 1 1c)1 0 0 00 0 0 00 0 1 1d)⋆1 0 3 00 1 2 00 0 0 10 0 0 0MATH 220 EXAM I, VERSION A PAGE 814. Find the parametric vector form of the solution set of the matrix equation Ax = 0 whereA =1 −1 0 3 30 0 1 −5 −30 0 0 0 0.a) x = x1−10430+ x300325b)⋆ x = x211000+ x4−30510+ x5−30301c) x = x211000+ x300301d) x = x2−30510+ x411000+ x50010315. Consider the matrix A =1 4 72 5 8−3 −9 −15. Which of the following vectors belong to thenull space of A?a) All vectors in R3.b)⋆ All vectors v in R3such that v1= v3= −v22.c)10−2.d) The zero vector only.MATH 220 EXAM I, VERSION A PAGE 916. Suppose A is an m × n matrix and all of its columns are pivot columns. Then, which of thefollowing statements is not necessarily true?a) The equation Ax = b has either a unique solution or none at all, for each vector bin Rm.b)⋆ The equation Ax = b is consistent for any vector b in Rm.c) The set of column vectors of A is a linearly independent set.d) The equation Ax = 0 has only the trivial solution.17. Let T be a linear transformation such that T11=23and T01=1−1.Find T45.a)39b)119c)−65d)⋆91118. If (A−1)T=1 −23 4, what is A?a)2 −0.3−0.2 0.1b)2 −31 1c)⋆0.4 −0.30.2 0.1d)4 −32 1MATH 220 EXAM I, VERSION A PAGE 1019. Let A =2 5−3 1and B =4 −53 k. What value(s) o f k, if any, will make AB = BA?a) 4b)⋆ 5c) 6d) Any real number20. Suppose T is the linear transformation given by Tx1x2=−5x1+ 9x24x1− 7x2. Is T one-to-one? Is T onto? Can you find T−1?a) T is one-to-one but not onto.b) T is onto but not one-to-one.c) T is one-to-one and onto, and T−1x1x2=−7x1− 9x2−4x1− 5x2.d)⋆ T is one-to-one and onto, and T−1x1x2=7x1+ 9x24x1+