## 1.8 Matrix Applications: Solving Systems of Equations

### Representing Systems of Equations in Matrix Form

- Matrices provide a concise way of representing systems of
**linear equations**(i.e. multiple related linear equations). The equations are represented in 3 matrices:- A
**square coefficient matrix**, generally denoted by a**capital A**, where each column lists the coefficients of a corresponding variable, while each row corresponds to a different equation. - A
**variable column matrix**which lists the variables. It is denoted by a**capital X**. This is multiplied by the coefficient matrix to form the left-hand side of the matrix equation. - A
**column matrix of constants**, which lists the constant in each equation. It is denoted by a**lower-case b**. This forms the right-hand side of the matrix equation. - Equation for a system of linear equations in matrix form:

- A

AX=b

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