Wesyu Posted January 17, 2005 Share Posted January 17, 2005 Find a 2x2 matrix A and a vector v in R2 such that the transforma- tion x --> Ax + v maps the triangle with vertices (1, 1); (2, -1); (3, 4) into the triangle with vertices (0, 0); (1, 0); (0, 1). How many different pairs (A, v) will do the job? Link to comment Share on other sites More sharing options...
Dave Posted January 18, 2005 Share Posted January 18, 2005 For the first part, it's pretty easy. Just find A and v s.t. (1,1) -> (0,0), (2,-1) -> (1,0) etc. Second part I haven't really thought about yet Link to comment Share on other sites More sharing options...
timo Posted January 19, 2005 Share Posted January 19, 2005 If I see it correctly, the number of possible solutions should become obvious when you solve the problem as you get a system of linear equations with six real-valued unknowns (four in A and two in v) and six equations (one for each coordinate mapped). Link to comment Share on other sites More sharing options...
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