Matrix Algebra; Systems Of Linear Equations With Three Unknowns - HP -11C Owner's Handbook Manual

Section 10: Applications Programs 149
Systems of Linear Equations
With Three Unknowns
This program uses Cramer's rule to solve systems of linear
equations with three unknowns. It has been included here because
of the relative ease with which it can be used to solve systems of
linear equations compared to the Matrix Algebra program.
Equations: A system of linear equations can be expressed as
AX=B.
ap; a2 a3
For three unknowns, A=\ a9 ag ag
a3y azz ags
X1 '-_bl
X= Xo B= b2
X3 b3
det A =ayj(agass — agzaszy) —aja(ag ass — assas;)
+a3(ag;agy —agas;) -
x;'s are solved by
_det (1)
! Det A
for Det A # 0 where det (1) is the determinant of the A matrix with
the it? column replaced by B.
Remarks: If Det A =0, then the system is linearly dependent and
this program is not applicable. The program will terminate with
Error 0. If Det A is very close to zero, the calculator representation
of the number will contain significant round-off error and the ratio
(det (i)/Det A) will be in error.