Let $T: \Bbb R^3 \rightarrow \Bbb R^3$ be the linear transformation given by reflecting across the plane $S=\{x:-x_1+x_2+x_3=0\}$ (...) 

Then, $S=\gen[(1,1,0),(1,0,1)]\$

But how can I get the matrix $R_v$ such that reflects across $S$? 

Thanks!


Question: executeQuery only working for queries when mySQL commands are uppercase?
Answer: 
Try using equalsIgnoreCase instead of straight equals.  
If you don't know if the code is getting into an if block, try adding some logging into that block.  
Assuming it is getting into the block, the query is likely causing the problem.