# HP 50g User Manual Page 349

Graphing calculator.

Let's store the latest result in a variable X, and the matrix into variable A, as
follows:
Press K~x` to store the solution vector into variable X
Press ƒ ƒ ƒ to clear three levels of the stack
Press K~a` to store the matrix into variable A
Now, let's verify the solution by using: @@@A@@@ * @@@X@@@ `, which results in
(press ˜ to see the vector elements): [-9.99999999992 85. ], close enough
to the original vector b = [-10 85].
Try also this, @@A@@@ * [15,10/3,10] ` ‚ï`, i.e.,
This result indicates that x = [15,10/3,10] is also a solution to the system,
confirming our observation that a system with more unknowns than equations is
not uniquely determined (under-determined).
How does the calculator came up with the solution x = [15.37... 2.46...
9.62...] shown earlier? Actually, the calculator minimizes the distance from a
point, which will constitute the solution, to each of the planes represented by the
equations in the linear system. The calculator uses a least-square method, i.e.,
minimizes the sum of the squares of those distances or errors.
Over-determined system
The system of linear equations
x
+ 3x
= 15,
1
2
2x
– 5x
= 5,
1
2
-x
+ x
= 22,
1
2
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