Talk:06-240/Classnotes For Tuesday November 14

Reduced row echelon form - Is there a reason to make column with entry 1 to the form of e_n (1 at n^th row, 0 for all other entries)? According to some books, matrix ${\begin{pmatrix}1&3&2&4&2\\0&1&2&3&4\\0&0&0&1&2\\0&0&0&0&0\end{pmatrix}}$ is good enough to show that the rank of the matrix is 3. This is because the first three rows are linearly independent, they can't form linear combination for preceeding rows. Anyone could tell why we have to reduce it to ${\begin{pmatrix}1&0&-4&0&-2\\0&1&2&0&-2\\0&0&0&1&2\\0&0&0&0&0\end{pmatrix}}$? Thank you. Wongpak 23:54, 15 November 2006 (EST)