Systems of linear algebraic equations occur abundantly in most fields of science and engineering.
- structural analysis (civil engineering)
- heat conduction (mechanical and chemical engineering)
- analysis of power grids (electrical engineering)
- production planning (economics)
- regression analysis (statistics)
One of the most common sources of linear algebraic is from the discretisation of ordinary or partial differential equations or integral equations.
A linear equation is an equation that can be expressed as,
a0x0 + a1x1 +
A finite set of linear equations is called a system of linear equations
or a linear system
. A set of numbers s0
is a solution to a linear system if and only if the substitutions a0
satisfies every equation in the system.
A linear system of n
linear equations in n