Proving every 2 × 3 linear system can be put into RREF by a series of row operations

Question

I'm trying to figure out why the following statemnt is valid

Every 2 × 3 linear system can be
put into RREF by a series of row
operations

I know this theorem but I'm not entirely sure how to apply it to the given statement

**Theorem REMEF Row-Equivalent Matrix in Echelon Form**  
Suppose A is a matrix. Then there is a matrix B so that
1. A and B are row-equivalent
2.B is in reduced row-echelon form

Answer 1

By the theorem you have stated, you have no restrictions on what the Matrix $A$ can be.

So for the specific case, let $A$ be a $2 \times 3$ matrix that represents the $2 \times 3$ linear system you have. From the theorem, there exists a matrix $B$ that $A$ and $B$ are row-equivalent and that $B$ is in RREF. Thus, your matrix $A$ can be reduced to $B$ by reducing the rows.