# HP 48gII User Manual Page 345

Graphing calculator.

Under-determined system
The system of linear equations
can be written as the matrix equation A⋅x = b, if
2
3
A
1
3
This system has more unknowns than equations, therefore, it is not uniquely
determined. We can visualize the meaning of this statement by realizing that
each of the linear equations represents a plane in the three-dimensional
Cartesian coordinate system (x
equations shown above will be the intersection of two planes in space. We
know, however, that the intersection of two (non-parallel) planes is a straight
line, and not a single point. Therefore, there is more than one point that
satisfy the system. In that sense, the system is not uniquely determined.
Let's use the numerical solver to attempt a solution to this system of equations:
‚Ï ˜˜˜ @@OK@@ . Enter matrix A and vector b as illustrated in the
previous example, and press @SOLVE when the X: field is highlighted:
2x
+ 3x
–5x
= -10,
1
2
3
x
– 3x
+ 8x
= 85,
1
2
3
x
1
5
,
x
,
x
and
2
8
x
3
, x
, x
). The solution to the system of
1
2
3
10
b
.
85
Page 11-19