Visualizing the minimization of $\|Ax-b\|_2^2$?

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Consider the least-squares problem

$$\text{minimize} \quad \|Ax-b\|_2^2$$

where $A$ is an $m \times n$ matrix and $b$ is an $m$-vector.

How does it looks like geometrically? Could someone draw a picture so I could visualize it?