MATH 220 NAME EXAM I STUDENT NUMBER SPRING 2011 INSTRUCTOR VERSION A SECTION NUMBER On your scantron write and bubble your PSU ID Section Number and Test Version Failure to 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 It is 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 ANY OTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THIS EXAMINATION THE USE OF NOTES OF ANY KIND IS NOT PERMITTED DURING THIS EXAMINATION MATH 220 EXAM I VERSION A PAGE 2 1 Solve the linear system 2x1 x2 3x3 a b c d 5 3x1 2x2 6x3 3 x1 x2 6 53 35 56 3 3 9 2 1 5 3 2 11 5 3 2 1 5 3 2 How many solutions does the following system have 3x1 5x2 4x3 1 2x1 2x2 x3 0 7x1 x2 6x3 2 a None b One c Infinitely many with 1 free variable d Infinitely many with 2 free variables MATH 220 EXAM I VERSION A PAGE 3 3 According to the graph how can we best describe the vector w in terms of the vectors u and v a 2v u b 3v u c 3v u d 2v u 4 For which value s of h is b 1 a2 0 a h 0 b h 1 c h 2 d h any real number 0 h in the set spanned by the vectors a1 2 1 and MATH 220 EXAM I VERSION A 5 Which of the following is a linearly independent set 0 a 2 2 4 2 b 3 0 0 1 4 3 3 3 2 1 1 5 0 c v 2v u 0 1 2 2 d 3 3 7 6 What is the standard matrix for rotation of the xy plane about the origin by 180 a 0 1 1 0 b 1 0 0 1 c 1 0 0 1 d 0 2 2 0 7 Which of the following matrices is invertible a 1 3 2 6 1 2 b 3 4 5 6 1 4 7 c 2 5 8 3 6 10 2 0 1 d 3 0 1 1 0 1 PAGE 4 MATH 220 EXAM I VERSION A PAGE 5 8 Find a basis of the column space Col A for the matrix 2 3 2 1 4 A 4 5 3 11 4 4 6 4 3 4 2 3 2 a 4 5 3 4 6 4 2 3 1 b 4 5 11 4 6 3 2 3 2 1 4 c 4 5 3 11 4 4 6 4 3 4 2 3 4 5 d 4 6 9 The following are augmented matrices of corresponding linear systems Which system is consistent when b b1 b2 b3 T is any vector in R3 a b c d 1 2 3 b1 4 5 6 b2 7 8 9 b3 1 2 3 b1 4 5 6 b2 6 8 10 b3 0 1 4 b1 2 3 2 b2 4 5 0 b3 1 3 4 b1 4 2 6 b2 3 2 7 b3 MATH 220 EXAM I VERSION A 10 Which of the following multiplications will give you a vector in R4 a a d a b e i 1 4 c 6 9 d 0 2 x b c y e f z w b c d x f g h y j k l z 2 5 x 8 y 12 1 4 3 3 2 1 w x y z 11 Which of the following is not a linear transformation a T x 3x x1 0 1 x1 b T x2 1 0 x2 x1 x1 x2 c T x2 x d T xy y PAGE 6 MATH 220 EXAM I VERSION A PAGE 7 2 5 0 4 6 1 3 4 1 12 Find the entries in the second row of AB where A 6 8 7 and B 7 3 2 3 0 9 a 5 1 b 5 1 c 2 3 d 2 3 13 Which of following matrices is in reduced echelon form 1 0 a 0 0 1 b 0 0 1 0 c 0 1 0 d 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 3 2 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 MATH 220 EXAM I VERSION A PAGE 8 14 Find the parametric vector form of the solution set of the matrix equation Ax 0 where 1 1 0 3 3 0 1 5 3 A 0 0 0 0 0 0 0 1 0 0 a x x1 4 x3 3 2 3 5 0 3 3 1 0 0 1 3 b x x2 0 x4 5 x5 0 1 0 1 0 0 0 1 0 1 x3 3 0 c x x2 0 0 1 0 0 1 3 0 1 0 d x x2 5 x4 0 x5 1 0 0 1 3 0 0 1 4 7 5 8 Which of the following vectors belong to the 15 Consider the matrix A 2 3 9 15 null space of A a All vectors in R3 b All vectors v in R3 such that v1 v3 1 c 0 2 d The zero vector only v2 2 MATH 220 EXAM I VERSION A PAGE 9 16 Suppose A is an m n matrix and all of its columns are pivot columns Then which of the following statements is not necessarily true a The equation Ax b has either a unique solution or none at all for each vector b in 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 4 Find T 5 3 a 9 11 b 9 6 c 5 9 d 11 1 T 18 If A a b c d 1 2 what is A 3 4 2 0 3 0 2 0 1 2 3 1 1 0 4 0 3 0 2 0 1 4 3 2 1 1 1 2 3 and T 0 1 1 1 MATH 220 19 Let A EXAM I VERSION A 2 5 3 1 and B PAGE 10 4 5 What value s of k if any will make AB BA 3 k a 4 b 5 c 6 d Any real number 20 Suppose T is the linear transformation given by T x1 x2 5x1 9x2 Is T one4x1 7x2 to one Is T onto Can you find …