Systems of Linear Equations

A linear equation in n variables (or unknowns) x1, x2, . . . , xn is one which can be expressed in the form

a1x1 + a2x2 + · · ·+ anxn = b (1)

where a1, a2, . . . , an and b are real numbers. The constants a1, a2, . . . , an are called the coefficients of the variables x1, x2, . . . , xn respectively.