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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Originally Posted by flawless

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

Then the new coordinates of the point are:





.

Therefore .....


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