- #1
ji707
- 8
- 0
hi all, i was given a take home exam for my linear algebra course and i can't seem to find the answer to this problem.
if [itex] A^T\vec{b} = \vec{0}[/itex]
what can you say about ##\hat{b}## the vector in Col A which is the best approximation of
##\vec{b}##.
##A^T A \vec{x} = A^T\vec{b}##
I don't even know where to start,
I have a feeling that there is a way to show that ##\hat{b}## is equal to ##\vec{b}##. but I don't know how to go about finding this.
I've been thinking about it for a day already. any hints or nudges in the right direction would be very helpful please.
Homework Statement
if [itex] A^T\vec{b} = \vec{0}[/itex]
what can you say about ##\hat{b}## the vector in Col A which is the best approximation of
##\vec{b}##.
Homework Equations
##A^T A \vec{x} = A^T\vec{b}##
The Attempt at a Solution
I don't even know where to start,
I have a feeling that there is a way to show that ##\hat{b}## is equal to ##\vec{b}##. but I don't know how to go about finding this.
I've been thinking about it for a day already. any hints or nudges in the right direction would be very helpful please.