MATH 220 NAME FINAL EXAM STUDENT NUMBER MAY 8 2008 INSTRUCTOR FORM A SECTION NUMBER This examination will be machine processed by the University Testing Service Use only a number 2 pencil on your answer sheet On your answer sheet identify your name this course MATH 220 and the date Code and blacken the corresponding circles on your answer sheet for your student I D number and the class section number Code in your test form There are 25 multiple choice questions each worth 5 points For each problem four possible answers are given only one of which is correct You should solve the problem note the letter of the answer that you wish to give and blacken the corresponding space on the answer sheet Mark only one choice darken the circle completely you should not be able to see the letter after you have darkened the circle Check frequently to be sure the problem number on the test sheet is the same as the problem number of the answer sheet THE USE OF A CALCULATOR CELL PHONE OR ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED DURING THIS EXAMINATION CHECK THE EXAMINATION BOOKLET BEFORE YOU START THERE SHOULD BE 25 PROBLEMS ON 14 PAGES INCLUDING THIS ONE MATH 220 FINAL EXAM FORM A PAGE 2 1 Find the general solution of the system whose augmented matrix is 1 7 0 6 5 0 0 1 2 3 1 7 4 2 7 x 5 7x2 6x4 1 x2 free a x3 3 2x4 x free 4 x 4 7x2 3x3 1 x2 free b x3 3 2x4 x free 4 x 5 7x2 1 x2 free c x3 3 x 0 4 d The system is inconsistent 1 3 h 0 1 2 Let v1 v2 and y 5 For which value s of h is y is in the plane 2 8 3 generated by v1 and v2 a h 7 b h 7 2 c For all values of h d There is no such value of h MATH 220 FINAL EXAM FORM A 1 3 0 3 1 1 1 1 3 Let A 0 4 2 8 and Then which of the following is true 2 0 3 1 a The columns of A span R4 b The columns of A span R3 c The matrix equation Ax b is consistent for all b in R4 d The matrix equation Ax 0 has more than one solutions 4 Describe the solution set of x1 2x2 9x3 5x4 0 x2 2x3 6x4 0 in parametric vector form 5 9 2 6 2 1 a x x2 0 x3 1 x4 0 1 0 0 5 9 2 6 2 0 b x x2 0 x3 0 x4 0 0 0 0 5 7 2 6 c x x3 1 x4 0 1 0 7 5 6 2 d x x3 0 x4 0 0 0 PAGE 3 MATH 220 FINAL EXAM FORM A PAGE 4 5 How many pivots does a 13 8 matrix A have if the columns of A are linearly independent a 5 b 8 c 13 d None of the above 6 Which of the following transformations is linear x1 x3 a T x2 x2 x3 x3 x1 x1 x1 x3 b T x2 x2 x3 x1 x2 0 x1 x c T x2 3 1 x3 x1 x1 d T x2 x2 x3 x3 MATH 220 FINAL EXAM FORM A PAGE 5 7 Let T R2 R2 be a linear transformation which reflects points through the vertical x2 axis and then rotates points 2 radians counterclockwise Find the standard matrix of T 0 0 1 a A 1 0 0 1 0 b A 0 1 0 0 1 c A 1 0 0 0 1 d A 1 0 0 0 1 2 1 2 1 8 If A and AB then what is the first column of B 2 5 6 9 3 0 1 a 1 0 8 b 5 0 7 c 4 d None of the above MATH 220 FINAL EXAM FORM A PAGE 6 9 14 3 9 Let A 2 4 1 Then which of the following is the third column of A 1 3 4 1 0 a 1 2 2 1 b 0 3 1 c 3 2 4 d A is not invertible 10 Let A be an invertible n n matrix Then which of the following statements is false a The columns of A are linearly independent b detA 0 c The linear transformation defined by T x Ax is onto d The equation Ax 0 has a non trivial solution MATH 220 FINAL EXAM FORM A PAGE 7 11 Which of the following sets is a subspace of R3 x1 x2 x1 x2 x3 0 a x3 x1 2 2 x2 x1 x2 0 b x3 x1 x2 x1 2x2 3x3 0 4x2 x3 0 c x3 x1 x2 x1 x2 x3 3 d x3 1 5 12 Given A 4 2 1 0 equivalent to 0 0 a b c d 2 4 3 3 10 9 7 8 find a basis for the column space of A if A is row 8 9 2 7 4 5 0 6 2 4 3 3 0 1 2 0 0 0 0 5 0 0 0 0 2 4 3 3 1 0 0 1 2 0 0 0 0 0 5 0 0 0 0 0 3 4 1 1 0 0 0 0 5 0 0 0 3 3 4 2 1 5 10 9 7 8 4 8 9 2 7 2 6 0 5 4 4 3 1 9 5 8 4 9 7 2 6 5 MATH 220 FINAL EXAM FORM A PAGE 8 1 13 Find the coordinate vector of x 1 with respect to the basis B v1 v2 v3 1 1 2 1 where v1 1 v2 4 and v3 2 0 0 1 a b c d 1 1 1 1 2 1 3 3 2 1 0 0 1 2 1 2 5 2 0 0 3 0 14 Compute the determinant of A 2 6 7 5 0 0 4 4 a 2 b 2 c 24 d 24 MATH 220 FINAL EXAM FORM A a 5 6 5 1 2 15 If det b 1 3 5 find det 3a 3b 3c c 2 7 6 3 7 a 15 b 15 c 5 3 d 5 3 4 1 6 16 Which of the following is an eigenvector of A 2 1 6 2 1 8 a b c d 4 1 8 1 0 0 1 1 0 1 1 1 PAGE 9 MATH 220 FINAL EXAM FORM A 1 0 1 17 Find the characteristic equation of A 3 4 1 1 0 2 a 1 4 2 b 4 2 3 c 4 2 3 d 1 4 3 0 2 1 18 Let A Which of the following matrices is similar to A 1 2 0 2 0 a D 0 2 0 1 0 b D 0 3 0 1 0 c …