Definition:Leading Coefficient (Matrix)

Definition

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

Consider:

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

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.