After performing Gram-Schmidt process for the following matrix:
$\pmatrix{3&2&3\\ 2&5&-1\\ 2&4&8\\ 12&2&1}$
the resultant matrix is this one:
$\pmatrix{0.23643312&0.18771349&0.22132104\\ 0.15762208&0.74769023&-0.64395812\\ 0.15762208&0.57790444&0.72904263\\ 0.94573249&-0.26786082&-0.06951101}$
I wonder why the last row of the above orthonormal matrix is not a zero vector? And what is more strange is that its dimensions(sum of all the norms) is 3. How can those three (column) vectors be in space? Is the space three-dimensional or four-dimensional?