I'm trying to solve this problem . but I don't know how to proceed except for the fact that I can replace x with $A^TA^{-1} A^Tb$. any help please?
Let A and à have full rank. Let x and $x̃$ be, respectively, the unique least- squares solutions to the problems Ax = b and $Ãx̃ = b$, where à = A + E. Then prove that
$\frac{||x~ - x ||}{||x^~}$ $\leq$ $Cond(A) \frac{||E||}{||A||}$ ($ 1 + \frac {||b||}{||A||||x^~||}$) + $Cond(A)^2 \frac{||E||}{||A||}(1+ \frac{||E||}{||A||})$