Results 1 to 2 of 2

Math Help - Linear Transformations and Invertibility

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    76

    Linear Transformations and Invertibility

    Which of the following linear transformations from R^3 to R^3 are invertible ?

    A. Projection onto the z-axis
    B. Rotation about the x-axis
    C. Dilation by a factor of 3
    D. Reflection in the origin
    E. Trivial transformation (i.e. T(v)=0 for all v)
    F. Identity transformation (i.e. T(v)=v for all v)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,525
    Thanks
    1384
    Quote Originally Posted by My Little Pony View Post
    Which of the following linear transformations from R^3 to R^3 are invertible ?

    A. Projection onto the z-axis
    B. Rotation about the x-axis
    C. Dilation by a factor of 3
    D. Reflection in the origin
    E. Trivial transformation (i.e. T(v)=0 for all v)
    F. Identity transformation (i.e. T(v)=v for all v)

    A) Any (x,y,5) is projected onto (0, 0, 5). What would the inverse transformation of (0, 0, 5) be? Or, is there any (x, y, z) that would be "projected" onto (1, 1, 1)?

    B) What happens if you rotate by angle \theta and then rotate by angle -\theta?

    C) What happens if you "dilate" by a factor of 3 and then "dilate" by a factor of 1/3?

    D) What happens if you reflect twice?

    E) So any (x, y, z) is tranformed to (0, 0,0). What would the inverse transform of (0, 0, 0) be? What would the inverse transform of (1, 1, 1) be?

    F) What happens if you apply this transformation twice?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Transformations and the General Linear Group
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 26th 2011, 10:50 AM
  2. Basic Linear Algebra - Linear Transformations Help
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 7th 2010, 03:59 PM
  3. Linear Independence in linear transformations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 17th 2009, 04:22 PM
  4. Linear Algebra: Linear Transformations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 9th 2008, 04:30 PM
  5. Replies: 3
    Last Post: June 2nd 2007, 10:08 AM

Search Tags


/mathhelpforum @mathhelpforum