{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

204PS42008 - Econ 204 Summer/Fall 2008 Problem Set 4 Due in...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 204, Summer/Fall 2008 Problem Set 4 Due in Lecture Tuesday, August 12 1. Show that each of the following is a vector space over R , find a Hamel basis, and the dimension of the space: (a) The set of solutions in R 3 to the following systems of linear equations x 1 2 x 2 + x 3 = 0 2 x 1 3 x 2 + x 3 = 0 (b) The set of all n × n matrices having trace 1 equal to zero. 2. T : M 2 × 3 M 2 × 2 defined by T a 11 a 12 a 13 a 21 a 22 a 23 = 2 a 11 a 12 a 13 + 2 a 12 0 0 Determine Ker ( T ), dim( Ker ( T )) and Rank ( T ). Is T one-to-one, onto, or neither? 3. Derive a transformation, T : R 2 R 2 , which reflects a point across the line y = 5 x . (a) First, calculate the action of T on the points (1 , 5) and ( 5 , 1). (b) Next, write the matrix representation of T using these two vectors as a basis. (c) Find S and S - 1 , the matrices that changes coordinates under this basis to standard coordinates and back again. (d) Write the matrix representation of T in the standard basis.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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