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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:

AX=b

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