System of Linear Equations - General Form

General Form

A general system of m linear equations with n unknowns can be written as

\begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \cdots + \;&& a_{1n} x_n &&\; = \;&&& b_1 \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \cdots + \;&& a_{2n} x_n &&\; = \;&&& b_2 \\ \vdots\;\;\; && && \vdots\;\;\; && && \vdots\;\;\; && &&& \;\vdots \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \cdots + \;&& a_{mn} x_n &&\; = \;&&& b_m. \\ \end{alignat}

Here are the unknowns, are the coefficients of the system, and are the constant terms.

Often the coefficients and unknowns are real or complex numbers, but integers and rational numbers are also seen, as are polynomials and elements of an abstract algebraic structure.

Read more about this topic:  System Of Linear Equations

Famous quotes containing the words general and/or form:

    “When General Motors has to go to the bathroom ten times a day, the whole country’s ready to let go. You heard of that market crash in ‘29? I predicted that.... I was nursing a director of General Motors. Kidney ailment, they said; nerves, I said. Then I asked myself, “What’s General Motors got to be nervous about?” “Overproduction,” I says. “Collapse.””
    —John Michael Hayes (b. 1919)

    “Man is a victim of dope
    In the incurable form of hope.”
    —Ogden Nash (1902–1971)