Matrix A has rank n iff diagnol entries of R' are non zero
Sorry about formatting as this is my first post here.
Question :- A mXn matrix (m>=n), A=Q'R' (Reduced QR)
To show that A has rank n iff diagonal entries of R' are non zero.
My Solution :-
if Ax = 0 => Q'R'x = 0 => R'x =0
let R' = upper triangular matrix (nXn) and x is a column vector.
suppose ..... are not 0
since R'x = 0 =>
but is not zero as is 0 and we can have = say 1 ....so we can determine value of by back substitution
=> x is a nonzero vector such that R'x = 0
I am not able to go beyond this.....Am I taking right approach..
Any help is appreciated.