# HP 50g User Manual Page 347

Graphing calculator.

To check that the solution is correct, enter the matrix A and multiply times this
solution vector (example in algebraic mode):
Under-determined system
The system of linear equations
can be written as the matrix equation A x = b, if
A
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
1
x
– 3x
1
2
3
5
,
1
3
8
, x
1
+ 3x
–5x
= -10,
2
3
+ 8x
= 85,
2
3
x
1
x
,
x
2
x
3
, x
). The solution to the system of
2
3
10
b
and
85
.
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