HP 50g User Manual page 347

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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