MATH 220 Name MIDTERM EXAMINATION OCTOBER 17 2001 ID Section There are multiple choice questions Each problem is worth 5 points Four possible answers are given for each problem only one of which is correct When you solve a problem note the letter next to 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 THE USE OF CALCULATORS DURING THE EXAMINATION IS FORBIDDEN CHECK THE EXAMINATION BOOKLET BEFORE YOU START THERE SHOULD BE PROBLEMS ON PAGES INCLUDING THIS ONE MATH 220 MIDTERM EXAMINATION PAGE 2 1 If 1 2 3 5 h 4 is the augmented matrix of a system of linear equations then for what value of h is the system inconsistent a h 0 b h 5 c h 10 d h 15 2 Which of the following matrices is in row echelon form 1 0 0 0 0 A 0 1 0 B 0 0 0 2 0 0 0 a A and C but not B b A and B but not C c B only d B and C but not A but not necessarily reduced row echelon 1 0 1 0 0 C 1 0 0 0 0 0 0 MATH 220 MIDTERM EXAMINATION PAGE 3 1 1 2 8 3 If A 1 2 3 1 then find the matrix in reduced row echelon form that is row 3 7 4 10 equivalent to A a b c d 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 2 0 0 3 1 0 1 0 1 2 0 0 1 1 0 2 0 1 3 0 0 5 1 0 7 0 0 6 1 2 7 4 If v1 1 and v2 1 then for what value of h does the vector v3 5 lie in 2 1 h the plane generated by v1 and v2 a h 4 b h 4 c h 8 d h 8 MATH 220 MIDTERM EXAMINATION 5 What is the solution set of the following system of linear equations 2x2 3x3 1 2x1 4x2 x3 2 6x1 12x2 3x3 5 a x1 1 x2 0 x3 1 b x1 3 2t x2 2 t x3 t c x1 2 2t x2 t x3 3 d There are no solutions The system is inconsistent 2 1 5 2 3 1 1 4 and v 6 If A 2 3 6 then what is the second entry of Av 0 2 4 6 3 a 1 b 2 c 3 d 4 PAGE 4 MATH 220 1 2 7 If A 1 of A MIDTERM EXAMINATION PAGE 5 6 3 12 2 then what geometric figure is formed from the span of the columns 3 0 a A line b A plane c All of R3 d All of R2 8 If A is a 4 by 4 matrix whose columns span R4 then which of the following statements is false a The equation Ax b has at least one solution for every b b The columns of A are linearly independent c The equation Ax 0 has a nontrivial solution d The linear transformation x 7 Ax is onto MATH 220 MIDTERM EXAMINATION PAGE 6 4 8 6 is the coefficient matrix of a system of linear equations then what is the 9 If A 3 2 4 solution set for the associated homogeneous linear system a x1 1 x2 2 b x1 0 x2 0 c x1 2x2 x2 t d There are no solutions because the the system is inconsistent 10 If T is the linear transformation defined by the formula T x1 x2 x2 x1 x1 3x2 x1 x2 then what is the standard matrix for T 0 1 1 1 a 1 0 3 1 1 0 3 1 b 0 1 1 1 0 1 1 0 c 1 3 1 1 1 0 0 1 d 3 1 1 1 MATH 220 MIDTERM EXAMINATION PAGE 7 11 If T R2 R2 is the linear transformation that first rotates points clockwise by 4 about the origin and then reflects points about the x1 axis then what is the standard matrix for T 1 1 1 a 2 1 1 1 1 1 b 1 1 2 1 1 1 c 2 1 1 1 1 1 d 2 1 1 12 If then what is AB a b c d 1 11 3 1 2 3 1 5 16 1 3 3 8 2 6 8 2 6 8 0 3 8 4 6 5 2 1 2 A 1 4 and B 3 1 3 0 MATH 220 MIDTERM EXAMINATION 2 3 2 1 13 If A and If B then for what value of h does AB BA 0 4 0 h a h 1 b h 2 c h 8 3 d h 3 8 8 6 14 If A then what is the inverse of A 9 7 a b c d 7 6 9 8 1 7 6 9 8 2 1 7 6 9 8 2 7 6 9 8 PAGE 8 MATH 220 MIDTERM EXAMINATION 2 0 0 15 If A 0 1 0 then what is the inverse of A 1 1 1 a b c d 1 2 0 0 0 1 0 1 2 1 1 1 2 0 0 0 1 0 0 1 1 1 2 0 0 0 1 0 1 2 1 1 1 2 0 0 0 1 0 1 2 1 1 1 1 16 If A then what is A3 2 1 a b c d 1 8 7 10 3 6 1 8 1 1 5 7 3 3 1 1 PAGE 9 MATH 220 MIDTERM EXAMINATION PAGE 10 17 Which of the following statements is true a If A is an invertible matrix then the columns of A are linearly independent b If A is an n by n matrix that has n pivot positions then the equation Ax 0 has a nontrivial solution c If AT is not invertible A is not invertible d If A is an n by n matrix then the linear transformation x 7 Ax is one to one then A is invertible T 1 18 If A a b c d 3 1 then what is A 5 2 2 5 1 1 5 3 5 2 5 1 3 2 5 1 5 1 3 5 3 5 1 2 MATH 220 MIDTERM EXAMINATION 19 Which of the following is a linear subspace of R3 a x1 x2 x3 x1 x2 x3 0 b x1 x2 x3 x1 x2 x3 0 c x1 x2 x3 x1 x2 x3 1 d x1 x2 x3 x1 x2 x3 x1 x2 x3 20 Which of the following is not a linear subspace of R3 a The null space of a 3 4 matrix b The column space of a 3 4 matrix c The null space …