We've been taught that the next equation:
$A^TAx= A^Tb$ , where $A\in\mathbb{R}^{m\times n}$ and $b\in\mathbb{R}^m$ are given and $x\in\mathbb{R}^n$ is the possible solution, has at least one solution.
I couldn't prove it myself. Is this lemma is correct? if so, how can I prove it?
I tried to rely on the property $\ker{(A)}=\ker{(A^T*A)}$ when proving.