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Summary: SOLVING LINEAR SYSTEMS
We want to solve the linear system
a1,1x1 + · · · + a1,nxn = b1
...
an,1x1 + · · · + an,nxn = bn
This will be done by the method used in beginning
algebra, by successively eliminating unknowns from
equations, until eventually we have only one equation
in one unknown. This process is known as Gaussian
elimination. To put it onto a computer, however, we
must be more precise than is generally the case in high
school algebra.
We begin with the linear system
3x1 - 2x2 - x3 = 0 (E1)
6x1 - 2x2 + 2x3 = 6 (E2)
-9x1 + 7x2 + x3 = -1 (E3)
3x1 - 2x2 - x3 = 0 (E1)
6x1 - 2x2 + 2x3 = 6 (E2)
-9x1 + 7x2 + x3 = -1 (E3)
[1] Eliminate x1 from equations (E2) and (E3). Sub-
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