midterm1_2009_answers

midterm1_2009_answers - Math 107 First Midterm Examination...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 107 First Midterm Examination February 18, 2009 NAME (Please print) Page Score 2 3 4 5 6 7 8 Total Instructions: 1. Do all computations on the examination paper. You may use the backs of the pages if necessary. 2. Put answers inside the boxes (when applicable). 3. Please signify your adherence to the honor code: I, , have neither given nor received aid in completion of this examination. 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
(10 Points) Score Solve 5 x 1 + 3 x 2 + x 3 = - 3 10 x 1 + 10 x 2 + 4 x 3 = - 2 15 x 1 + 17 x 2 + 10 x 3 = 5 We can factor 5 3 1 - 3 10 10 4 - 2 15 17 10 5 5 3 1 - 3 2 4 2 4 3 8 7 14 5 3 1 - 3 2 4 2 4 3 2 3 6 Let us check this factorization: 1 2 1 3 2 1 5 3 1 4 2 3 = 5 3 1 10 10 4 15 17 10 Then we back-solve 5 3 1 4 2 3 x 1 x 2 x 3 = - 3 4 6 = x 1 x 2 x 3 = - 1 0 2 Let us check the back-solve: 5 3 1 4 2 3 - 1 0 2 = - 3 4 6 Let us check the solution in the original linear system: 5 3 1 10 10 4 15 17 10 - 1 0 2 = - 3 - 2 5 70% of the class solved this problem correctly. answer = x 1 = - 1 , x 2 = 0 , x 3 = 2 . 2
Image of page 2
(25 Points) Score Suppose that we have factored A = LU where L = 1 4 1 7 3 , U = 2 5 8 - 24 4 16 - 32 1. (2 points) What is the dimension of the range of A (also called the column space of A)? 78% of the class solved this problem correctly. answer = 2 = r . 2. (2 points) What is the dimension of the nullspace of A? 74% of the class solved this problem correctly. answer = 2 = n-r . 3. (2 points) What is the dimension of the nullspace of A ? 17% of the class solved this problem correctly. answer = 1 = m-r . 4. (6 pts) Find a basis for the range of A. 61% of the class solved this problem correctly.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern