Thread: Linear transformation of vectors

I am in a matrix and power series class and I need to figure out how to answer the following type of question. I have read and reread the procedure the book uses and am still unable to figure this type of problem out,

I need to find all vectors in R^2 that satisfy T(v) = [-2 12 -20] or show that no such vector exists. The linear transformation T: R^2 ---> R^3 has matrix

A = [ 1 -3 1 ] T
[ 2 -8 8]

Could someone please show me the steps to attack this with? Thanks very much, Frostking

Originally Posted by Frostking

I am in a matrix and power series class and I need to figure out how to answer the following type of question. I have read and reread the procedure the book uses and am still unable to figure this type of problem out,

I need to find all vectors in R^2 that satisfy T(v) = [-2 12 -20] or show that no such vector exists. The linear transformation T: R^2 ---> R^3 has matrix

A = [ 1 -3 1 ] T
[ 2 -8 8]

Could someone please show me the steps to attack this with? Thanks very much, Frostking

This is a non-homogenoues linear system 3 x 2 (3 equations and 2 variables). Such a thing not always has a solution:



If now you solve the first two equations as we used to do in 8th or 9th grade, we get the unique solution . If you now plug in these two values in the 3rd equation you'll see you get an equality ==> there does exist a solution for the problem and it is unique (because it is unique for the first two eq's.)

Tonio