Linear Algebra with Applications

Info icon This preview shows page 1. Sign up to view the full content.

Name: Tuesday section time: Student ID: Math 20F - Linear Algebra - Winter 2003 Quiz #5 — February 18 (Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.) (Do not calculate more than is necessary to answer a problem! For one of these problems the answer(s) should be obvious from inspection.) 1. Let v 1 = (1 , - 1) T and v 2 = (1 , 2) T , so v 1 , v 2 are a basis for R 2 . Let x = (3 , 2) T . What are the coordinates x with respect to the basis v 1 , v 2 ? METHOD: You need to find a 1 , a 2 so that x 1 = a 1 v 1 + a 2 v 2 . For this you solve the matrix equation 1 1 - 1 2 a 1 a 2 = 3 2 . This can be done either by row operations, or by inverting the 2 × 2 matrix. ANSWER: The coordinates of x w.r.t. the basis v 1 , v 2 are ( 4 3 , 5 3 ) . That is, x = 4 3 v 1 + 5 3 v 2 . 2. Let
Image of page 1
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