Question

Find a permutation matrix p so that p a = lu. a = 1 2 4 3 6 8 0 9 0?

Answer 1

To find a permutation matrix p such that p a = lu, we need to determine the row and column swaps required to convert matrix a into matrix lu.

Step-by-step explanation:

A permutation matrix is a square matrix with exactly one entry of 1 in each row and column and 0 elsewhere. To find a permutation matrix p such that p a = lu, we need to determine the row and column swaps required to convert matrix a into matrix lu. Let's perform row and column swaps step by step:

1. First, we need to identify the positions of 1's in matrix a. The positions are:
   a(1,2), a(2,4), a(4,3), a(5,1), a(6,3), a(6,4).
2. Next, we perform row swaps to move the 1's to the correct positions in lu.
   For example, swap rows 1 and 5, rows 2 and 4, rows 3 and 6.
3. Finally, we perform column swaps to move the 1's to the correct positions in lu.
   For example, swap columns 2 and 5, columns 3 and 6.

The resulting permutation matrix p is obtained by performing the row and column swaps to the identity matrix.