(A = {{3,4,-5,2,1},{-3,1,-1,12,4},{2,-5,3,1,-3},{6,3,3,3,7}})//MatrixForm

A[[1]]

A[[All,1]]//MatrixForm

(A1={1/3 A[[1]],A[[2]],A[[3]], A[[4]]})//MatrixForm

(A2={ A1[[1]],A1[[2]]+3A1[[1]],A1[[3]]-2A1[[1]], A1[[4]]-6A1[[1]]})//MatrixForm

(A3={ A2[[1]],1/5A2[[2]],A2[[3]], A2[[4]]})//MatrixForm

(A4={ A3[[1]]-4/3A3[[2]],A3[[2]],A3[[3]]+23/3A3[[2]], A3[[4]]+5A3[[2]]})//MatrixForm

(A5={ A4[[1]],A4[[2]],-15/43A4[[3]], A4[[4]]})//MatrixForm

(A6={ A5[[1]]+1/15A5[[3]],A5[[2]]+6/5A5[[3]],A5[[3]], A5[[4]]-7A5[[3]]})//MatrixForm

(A7={ A6[[1]],A6[[2]],A6[[3]],43/2778 A6[[4]]})//MatrixForm

(A8={ A7[[1]]+153/43A7[[4]],A7[[2]]+260/43A7[[4]],A7[[3]]+317/43A7[[4]],A7[[4]]})//MatrixForm

RowReduce[A]//MatrixForm

(B = {{5,4,6,2},{3,-2,4,-1}})//MatrixForm

(B1 = {B[[1]]/5, B[[2]]})//MatrixForm

(B2 = {B1[[1]], B1[[2]]-3B1[[1]]})//MatrixForm

(B3 = {B2[[1]], -5/22B2[[2]]})//MatrixForm

(B4 = {B3[[1]]-4/5B3[[2]], B3[[2]]})//MatrixForm