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Math Help - linear algebra transformations

  1. #1
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    linear algebra transformations

    Consider the transformation T:R^2 ->R^2, where T(x,y)=((9/10)x+(3/10)y , (3/10)x+(1/10)y)
    (a)Show that every point in the plane is mapped to some point on the line 3y=x (this is the line where every point is mapped by T to itself)
    (b)give two or more reasons why the map T has no inverse.

    If someone could help me that would be great, i cannot do it. Thanks in advance


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  2. #2
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    Quote Originally Posted by flawless View Post
    Consider the transformation T:R^2 ->R^2, where T(x,y)=((9/10)x+(3/10)y , (3/10)x+(1/10)y)
    (a)Show that every point in the plane is mapped to some point on the line 3y=x (this is the line where every point is mapped by T to itself)
    (b)give two or more reasons why the map T has no inverse.

    If someone could help me that would be great, i cannot do it. Thanks in advance

    (a) Consider the transformation of the point (a, b).

    Then the new coordinates of the point are:


    x = \frac{9}{10} a + \frac{3}{10} b


    y = \frac{3}{10} a + \frac{1}{10} b = \frac{x}{3}.

    Therefore .....


    (b) Well, one reason would be that the transformation matrix has no inverse .......
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