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Math Help - Urgent help needed with linear algebra problem

  1. #1
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    Urgent help needed with linear algebra problem

    Hi

    I have a linear algebra problem which I need urgent assistance with.

    I'm present with something called a translation (x,y) \rightarrow (x+3,y+5). I'm tasked with showing that this "translation" can't be done as a linear mapping using regular coordinants.

    Any hints/idear on how I do that ????

    Hope and pray to hear from You.

    Sincerely and Best Regards,

    Fred
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  2. #2
    hpe
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    Suppose this were a linear mapping. Then if (a_1,b_1) \to (c_1,d_1) as well as  (a_2,b_2) \to (c_2,d_2) , it would follow that (a_1+a_2,b_1+b_2) \to (c_1+c_2,d_1+d_2) . (Check the definition of linearity in your notes.)

    Now try this for your mapping:
     (1,1) \to (4,6) and (2,2) \to (5,7) , but <br />
(1+2,1+2) = (3,3) \to (6,8) \ne (4+5,6+7).

    Thus the mapping is not linear.
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  3. #3
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    Hello hpe and many thanks for Your answer,

    How do I then prove that the mapping can be done using homogeneous coordinants ??

    Sincerely

    Fred

    Quote Originally Posted by hpe
    Suppose this were a linear mapping. Then if (a_1,b_1) \to (c_1,d_1) as well as  (a_2,b_2) \to (c_2,d_2) , it would follow that (a_1+a_2,b_1+b_2) \to (c_1+c_2,d_1+d_2) . (Check the definition of linearity in your notes.)

    Now try this for your mapping:
     (1,1) \to (4,6) and (2,2) \to (5,7) , but <br />
(1+2,1+2) = (3,3) \to (6,8) \ne (4+5,6+7).

    Thus the mapping is not linear.
    Last edited by Mathman24; June 15th 2005 at 05:18 AM.
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