the question highlighted below is in two parts, really have no clue how to start it, any help would be greatly appreciated!!

a. Recall that an elementary permutation matrix is an n x n matrix which is In except that two rows of

In have been swapped. If $\displaystyle P_{i;j}$ is the elementary permutation matrix where rows i and j have been swapped

and $\displaystyle A$ is a matrix (with n rows), describe the relationship between $\displaystyle A$ and $\displaystyle P_{i;j}A$.

b. Let A be the matrix:

$\displaystyle A=\left[\begin{array}{ccc}1&2&3\\2&4&6\\1&3&5\end{array}\r ight] $

Find a permutation matrix P, a lower triangular matrix L and an upper triangular matrix U so that

$\displaystyle A = P^{T}LU$:

thank you!