# linear algebra transformations

• April 19th 2008, 03:37 AM
flawless
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

• April 19th 2008, 03:54 AM
mr fantastic
Quote:

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

(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 .......