11. In fact Gaussian elimination shows there is a unique such that is upper triangular. 12. The Gaussian elimination algorithm remains applicable. 13. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form. 14. The simplest one is Gaussian elimination . 15. While the determinant can be computed in polynomial time by Gaussian elimination , the permanent cannot. 16. In essence, the TNC decoding process, like the LNC decoding process involves Gaussian elimination . 17. Gaussian elimination will produce incorrect results if it cannot correctly determine if a pivot is identically zero.18. We could solve this equation with a technique like Gaussian elimination , but this is too expensive. 19. The Gaussian elimination algorithm for obtaining LU decomposition has also been extended to this most general case. 20. The easier the method the better ( I'm not keen on coding gaussian elimination ).