There I have found from an old tutorial notes from a Linear Algebra course I am taking that I am finding the question rather cumbersome. I haven't come across any elementary matrices problem set in this way before. I have tried to using Gauss-Jordan Elimination to reduce matrix A, whilst performing the row operations on the corresponding elementary matrix. Although, I am unsure if this is the correct approach as the problem notes that RREF calculation is not necessary.
If [A|b] denotes the augmented matrix which corresponds to the system of linear equations
determine the matrix E such that [EA|Eb] is the reduced row echelon form of [A|b]. Note: You are asked to calculate the matrix E but you are not asked to calculate the reduced row echelon form.
Any help on how to approach this question or determine the matrix E would be highly appreciated.