# Definition:Leading Coefficient of Matrix

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## Definition

Let $\mathbf A = \sqbrk a_{m n}$ 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.

## Examples

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.

## Also see

• Results about leading coefficients can be found here.