The basic problem of linear algebra is to solve a system of linear equations.
A linear equation in the
n variables—or unknowns—
x1,
x2, …, and
xn
is an equation of the form
where
b and the coefficients
ai
are constants. A finite collection of such linear equations is called a
linear system. To
solve a system means to find all values of the variables that satisfy all the equations in the system
simultaneously. For example, consider the following system, which consists of two linear equations in two unknowns:
Although there are infinitely many solutions to each equation separately, there is only one pair of numbers
x1 and
x2 which satisfies both equations at the same time. This ordered pair, (
x1,
x2) = (2, 1), is called the
solution to the system.
Vector Algebra
Linear Systems
