Finding a matrix from 3 consecutive point transformations

[ConnorK]

Hello. I have come across a problem in my math textbook that i cannot solve. The question is worded as follows:

"A linear transformation T maps the point (1, 3) to the point (-2, -3) to the point (2, 4) to the point (-3, -11). find the matrix of the transformation."

I understood the question to mean the transformation matrix has to map the point (1, 3) to (-2, -3), the point (-2, -3) to the point (2, 4) and the point (2, 4) to the point (-3, -11).

I have tried multiple times to find the matrix that maps all the point but i cant find one.

 

[blamocur]

I have tried multiple times to find the matrix

Why don't you post what you've tried? This way we can have a better idea what kind of help you need.

 

[blamocur]

Also, unless I screwed up my own computations, the matrix which transforms (1,3) to (-2,-3) to (2,4) will transform (2,4) to (-8/3, -14/3), not to (-3,-11). Do you actually mean a linear transformation and not an affine one?

 

[ConnorK]

Why don't you post what you've tried? This way we can have a better idea what kind of help you need.

The "c" and "d" answers were correct but not the "a" and "b" ones.

 

[ConnorK]

Also, unless I screwed up my own computations, the matrix which transforms (1,3) to (-2,-3) to (2,4) will transform (2,4) to (-8/3, -14/3), not to (-3,-11). Do you actually mean a linear transformation and not an affine one?

This is the exact wording of the question, beyond this i cannot say anything more.

 

[blamocur]

The "c" and "d" answers were correct but not the "a" and "b" ones.

How do you know which ones are correct? Do you have answers in the book? If you do can you post the answers?
Thanks.

 

[blamocur]

Did you notice that you have 3 equations for a & b and 3 equations for c & d? I.e., there are more equations than unknowns.

 

[BeansNRice]