Question about a hamming (7,4) code

ComputerGeek

how can a 3 space vector tell you where the error occurred in your 7 space message vector?

will the vector produced when you run your message vector through your H matrix produce a binary value that corresponds to the bit location?

so the vector


[tex]\begin{matrix}
1\\
1\\
0
\end{matrix}
[/tex]

correspond to an error in bit 3 of your message vector and as such you just add the e3 vector to your message to correct the problem?