Elementary row operation on stacked matrix

Dependencies:

1. Elementary row operation
2. Stacking

Let $f$ be an elementary row operation. Then $f([A|B]) = [f(A)|f(B)]$.

Since $[A_1|A_2|\ldots|A_n] = [A_1|[A_2|[\ldots|A_n]\ldots]]$, this result can be generalized to $f([A_1|A_2|\ldots|A_n]) = [f(A_1)|f(A_2)|\ldots|f(A_n)]$.

Proof

A row operation on $[A|B]$ is equivalent to applying that row operation on $A$ and $B$ in parallel.

(Full proof yet to be written)

Dependency for: None

Info:

• Depth: 4
• Number of transitive dependencies: 6

Transitive dependencies:

1. Group
2. Ring
3. Semiring
4. Matrix
5. Stacking
6. Elementary row operation