Question

Perhaps there's an error in answer to problem 3.3.5 in Dr. Strang's book "Introduction to Linear Algebra" 4-th edition. The answer says that R1=A1 and R2=A2, but I think it's more general: R1=E*A1 and R2=E*A2.

Consider following matrices:

A1:
1 2 3
1 2 3

A2:
0 1 2
0 1 2

Corresponding reduced echelon forms are:

R1:
1 2 3
0 0 0

R2:
0 1 2
0 0 0

Which were obtained using following elimination matrix:

R1 = E * A1
R2 = E * A2

E:
1 0
-1 1

Now let's take a sum:

A1+A2:
1 3 5
1 3 5

rref(A1+A2):
1 3 5
0 0 0

Which exactly equals to sum of R1 and R2:

R1+R2:
1 3 5
0 0 0

Thanks!