Elementary row operation

Dependencies:

1. Matrix

Let $A$ be an $m$ by $n$ matrix.

Then the following are considered elementary row operations:

• $\langle i \rangle \leftarrow c\langle i \rangle$: Multiply the $i^{\textrm{th}}$ row by a non-zero scalar $c$.
• $\langle i \rangle \leftarrow \langle i \rangle + c\langle j \rangle$ where $i \neq j$: Add a multiple of the $j^{\textrm{th}}$ row to the $i^{\textrm{th}}$ row.
• $\langle i \rangle \leftrightarrow \langle j \rangle$: Swap the $i^{\textrm{th}}$ row with the $j^{\textrm{th}}$ row.

Dependency for:

1. Row equivalence of matrices
2. Every elementary row operation has a unique inverse
3. Elementary row operation on stacked matrix
4. Determinant after elementary row operation

Info:

• Depth: 3
• Number of transitive dependencies: 4

Transitive dependencies:

1. Group
2. Ring
3. Semiring
4. Matrix