Can Two Points Determine a Linear Transformation Matrix?

[LovePhys]

Hello everyone, I am a year 10 student. I am working on Transformation and there are 2 problems in the book that I actually have no idea to solve. Unfortunately, I am going to have a sudden exam in the next three days.

Hope that somebody can help me, thank you a lot! Or If you have any books which is appropriate with high school students, I am glad to read it!

1/ The images of 2 points are given for a linear transformation. Investigate whether this is sufficient information to determine the matrix of the transformation.
2/ Find the matrix of the linear transformation such that (1,0) -> (1,1) and (0,1) -> (2,2). What is the range of this transformation? (I found the matrix of the linear transformation).

Thank you,
Huyen Nguyen

 

[lanedance]

1/ start by trying to write down an arbitrary linear transformation based on the known image of 2 known points

2/ note tht every point will bee mapped onto a line - can you find the equation of the line