Sp07_midterm2 - Name Discussion Section No PID Time Midterm...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Name: PID: Discussion Section - No: Time: Midterm 2, Math 20F - Lecture B (Spring 2007) Duration: 50 minutes This is a closed-book exam. Calculators are not allowed. You can use one page of notes. To get full credit you should support your answers unless otherwise is stated. There are four questions in this exam. 1. An n × n matrix A is called skew-symmetric if A T = - A . Specifically the set of 2 × 2 skew-symmetric matrices is given by S 2 × 2 = 0 - a a 0 : a R . Let T : L 2 × 2 S 2 × 2 be the transformation from the 2 × 2 lower triangular matrices onto the 2 × 2 skew-symmetric matrices defined as T b 0 a c = 0 - a a 0 . where a , b , c are real numbers. a) (1 point) Show that S 2 × 2 is a one-dimensional subspace of 2 × 2 matrices. Find a basis for this subspace. b) (2 points) Show that T is a linear transformation. # Score 1 2 3 4 Total
Image of page 1

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

View Full Document Right Arrow Icon
c) (2 points) Find a basis for the kernel of T . 2. (Each part is 1 point) Determine whether each of the following statements is true or false. For each part circle either T (true) or F (false).
Image of page 2
Image of page 3
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