ABSTRACT
The central problem of linear algebra is the problem of solving a system of linear equations. References to solving simultaneous linear equations that derived from everyday practical problems can be traced back to Chiu Chang Suan Shu’s book Nine Chapters of the Mathematical Art, about 200 B.C. [Smoller, 2005]. Such systems arise naturally in modern applications such as economics, engineering, genetics, physics, and statistics. For example, an electrical engineer using Kirchhoff’s law might be faced with solving for unknown currents x, y, z in the system of equations:
1.95x + 2.03y + 4.75z = 10.02 3.45x + 6.43y − 5.02z = 12.13 2.53x + 7.01y + 3.61z = 19.46 3.01x + 5.71y + 4.02z = 10.52
Here we have four linear equations (no squares or higher powers on the unknowns) in three unknowns x, y, and z.Generally, we can consider a system of m linear equations in n unknowns:
a11x1 + a12x2 + · · · + a1nxn = b1 a21x1 + a22x2 + · · · + a2nxn = b2 a31x1 + a32x2 + · · · + a3nxn = b3 ...
