# Thread: what is the dimension of the range

1. ## what is the dimension of the range

T:R^n-->R defined by Tx=c1x1+...+cnxn..where atleast one of the c's is nonzero and x is in R^n..
then what is the dimension of image(T)?

2. Since this is a function to R, the dimension of the range is at most 1. Since "at least one of the c's is nonzero" T does not map every vector to 0 so the dimension of the range is at least 1.