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

Info iconThis 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 , Fnd 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 deFned by T a 11 a 12 a 13 a 21 a 22 a 23 = 2 a 11 a 12 a 13 +2 a 12 00 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 re±ects a point across the line y =5 x . (a) ²irst, 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) ²ind 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. (e) Use the point (
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online