Discussion & Conclusions

1. In terms of performance with respect to processing time, Method A - Matlab's 'backslash' command is the hand's down winner, followed by Method B - Matlab's inverse command. Use of Method C - Cramer's Rule is a very distant third, especially for large matrices (high values of n).
   
   
   • It was not possible to perfom any Method A, B, or C comparisons for n=10,000; this was due only to insufficient computer memory.
     
     
2. In terms of performance with respect to accuracy, without comparing every single vector element to its peer in the respective other methods, I used the 2-norm to deduce if the solution vectors were roughly the same. For low values of n (n=10, n=100), the 2-norms were the same for all three methods.
   
   
   • The 2-norms for Method A and B were equivalent. From this one can infer equal degrees of accuracy.
     
     
   • The 2-norm computed for a moderately large system (n=1000) "blew up" , returning the value NaN. I cannot provide an explanantion for this anomaly.
     
     
3. General conclusion for large or small system of equations, Method A rules supreme and is preferred! Method C is deprecated.