Results 1 to 3 of 3

Thread: Describing a transformation with a matrix

  1. #1
    Newbie
    Joined
    Sep 2016
    From
    West Yorkshire
    Posts
    7

    Describing a transformation with a matrix

    Hello

    I am working on a question from a textbook about a matrix transformation. Here is the question:
    Describing a transformation with a matrix-2017-02-07-21.22.31.jpg
    I have completed the question but I disagree with the answer given in the back of the book for part (b).
    I have worked out that the transformation represents a reflection in the line y=5^(-0.5) x followed by an enlargement scale factor 3.

    However the book says it is a reflection in the line y=x tan 48.2 followed by an enlargement scale factor 3.

    I have double checked my work and am sure I am correct. Could someone please look at my working and advise who is correct? Many thanks for looking at this.

    Here is my working:
    Describing a transformation with a matrix-2017-02-07-21.23.10.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,155
    Thanks
    3672

    Re: Describing a transformation with a matrix

    I agree with your solution ...

    Started with the vector $\langle 0,a \rangle$, $a > 0$

    $\begin{bmatrix}
    2 & \sqrt{5}\\
    \sqrt{5}& -2
    \end{bmatrix} \cdot
    \begin{bmatrix}
    0\\ a
    \end{bmatrix}=
    \begin{bmatrix}
    \sqrt{5} \cdot a\\ -2a
    \end{bmatrix}$

    $\bigg|\langle 0,a \rangle \bigg|=a$ and $\bigg|\langle \sqrt{5} \cdot a,-2a \rangle \bigg|=3a$

    $\langle 0,a \rangle$ has direction $\theta = 90^\circ$

    $\langle \sqrt{5} \cdot a,-2a \rangle$ has direction $\phi = \arctan\left(-\dfrac{2}{\sqrt{5}}\right) \approx -41.8^\circ$

    $\dfrac{\theta+\phi}{2} = \arctan\left(\dfrac{1}{\sqrt{5}}\right) \implies m = \dfrac{1}{\sqrt{5}} \text{ for } y=mx$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2016
    From
    West Yorkshire
    Posts
    7

    Re: Describing a transformation with a matrix

    Thank you very much. I thought the book was wrong. Thanks for clearing this up!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix transformation
    Posted in the Advanced Algebra Forum
    Replies: 13
    Last Post: Aug 3rd 2010, 10:50 AM
  2. Matrix transformation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Aug 3rd 2010, 07:04 AM
  3. Describing explicitly a linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Feb 23rd 2010, 06:14 AM
  4. Transformation Matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Jun 22nd 2009, 04:15 AM

/mathhelpforum @mathhelpforum