Question

True or False. Please explain your answer. If T: R^n --> R^n where T(X) = Ax, then the reduced echelon form of A is I. Thank you.

Answer 1

Is A independant or not?

Answer 2

Yes.

Answer 3

if A is a basis for R^n (efficient span); then yes, it row reduces to I (the identity matrix)

Answer 4

but without knowing if the arrow is meant to define a function from R^n ONTO R^n, or from R^n INTO R^n ... i wouldnt know how respond.

Answer 5

spose A = 2 4
1 2

for any x,y in R^2 we have: (2x+4y)
(x+2y)

which is a vector IN R^2, but since A is not independant, we are not ONTO R^2

Answer 6

Thank you.