48/50 Linear System Solver

[Werner]

There are a few issues here..
for me, my flag settings are as follows:
-20 Clear (underflow -> 0)
-21 Set (Overflow -> error)
-22 Clear (Infinite -> error)
Then there's another flag that influences the outcome: -54 Use tiny element.

With flag -54 Clear (Tiny element ->0), the 'stack solve' (/) returns Infinite Result, and the interactive Linear Solver will return the minimum norm Least Squares solution, because the system is underdetermined.
In this mode, the determinant is returned as 0 exactly, because there's a check to see if the matrix contains integers only, and with flag -54 clear, the calculator knows the determinant must be integer and will round the result to the nearest integer.
While solving systems, elements less than 1e-14 (relative size) will be set to zero.

With flag -54 Set (use tiny element), both methods will return

[ -5.41666..e14 -2.0833..e14 -1.25..e14]

The determinant now is calculated as -1.2e-13, due to roundoff. So the system is considered NOT singular, and a result can be produced.
In any case, it pays to compute the condition number (COND) that returns 9.8e15.
As a rule of thumb, the exponent signifies the number of wrong digits in your result, indicating here that the matrix is singular to working precision.

Werner


In any case