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can be written as the matrix equation A⋅x = b, if
This system has more equations than unknowns (an over-determined system).
The system does not have a single solution. Each of the linear equations in
the system presented above represents a straight line in a two-dimensional
Cartesian coordinate system (x
1
, x
2
). Unless two of the three equations in the
system represent the same equation, the three lines will have more than one
intersection points. For that reason, the solution is not unique. Some numerical
algorithms can be used to force a solution to the system by minimizing the
distance from the presumptive solution point to each of the lines in the system.
Such is the approach followed by the calculator numerical solver.
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:
To see the details of the solution vector, if needed, press the @EDIT! button. This
will activate the Matrix Writer. Within this environment, use the right- and left-
arrow keys to move about the vector:
.
22
5
15
,,
11
52
31
2
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−= bxA and
x
x
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