Given

A=⎡⎣⎢(1,3,1),(2,7,4),(3,8,5)⎤⎦⎥,

find elementary matrices E1, E2, E3
such that

E3E2E1A=U,

where U is an upper triangular matrix. Make your first
step E1 puts a 0 in the (3,1) position. (Notice that
A can be put in upper triangular form by three elementary
row operations. Find elementary matrices corresponding to each of
them. Remember order is important!)
E1=
E2=
E3=

(All blanks must be filled in to receive any credit on this
one.)

Now notice that A=LU, where
L=(E3E2E1)^−1.
Compute L= .
Notice that L is lower triangular with ones on the
diagonal. This is called the LU factorization of
A.