Definition:Simultaneous Linear Equations/Matrix Representation/Matrix of Coefficients

Definition

Consider the system of simultaneous linear equations can be expressed as:

$\ds \forall i \in \set {1, 2, \ldots, m} : \sum_{j \mathop = 1}^n \alpha_{i j} x_j = \beta_i$

expressed in matrix representation as:

$\mathbf A \mathbf x = \mathbf b$

The matrix $\mathbf A$ is known as the matrix of coefficients of the system.

Also known as

A matrix of coefficients is also known as a coefficient matrix.

Also see

• Solution to Simultaneous Linear Equations

• Results about simultaneous linear equations can be found here.

Sources

• 1982: A.O. Morris: Linear Algebra: An Introduction (2nd ed.) ... (previous) ... (next): Chapter $1$: Linear Equations and Matrices: $1.3$ Applications to Linear Equations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): augmented matrix
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): matrix of coefficients
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): augmented matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): matrix of coefficients
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): matrix of coefficients