Definition:Leading Coefficient of Matrix

Let $$\mathbf{A} = \left[{a}\right]_{m n}$$ be an $m \times n$ matrix.

The leading coefficient of each row of $$\mathbf{A}$$ is the leftmost non-zero element of that row.

A zero row has no leading coefficient.

Example
Let $$\mathbf{A} = \begin{bmatrix} 1 & 5 & 4 & 2 \\ 0 & 0 & 5 & 7 \\ 0 & 6 & 0 & 9 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix} $$.


 * The leading coefficient of row $$1$$ is $$1$$.
 * The leading coefficient of row $$2$$ is $$5$$.
 * The leading coefficient of row $$3$$ is $$6$$.
 * Row $$4$$ has no leading coefficient.