1) Answer following 8

1) Answer following 8. Find the permutation matrix P and elementary matrices El , E2, for a given matrix A such that PEZE1 A will perform following tasks on A: subtract the 3*2"d row from the 5""1St row (i.e: R1 = 5"'R1 — 3""R2 ), Then subtract 3"1 row from 8 * 2"d rows (i.e: R'2 = 8"'R2 - R3 );. Now Swap the second row and the third row N.B: P, E, E2, andA are 3x3 matrices b. For square A and A = LU with U having nonzero diagonal entries, Ax = b has a unique solution for all b. Here L and U are the matrices obtained by the LU decomposition.