HP 48gII User Manual page 350

• If A is a square matrix and A is non-singular (i.e., it's inverse matrix
exist, or its determinant is non-zero), LSQ returns the exact solution to
the linear system.
• If A has less than full row rank (underdetermined system of equations),
LSQ returns the solution with the minimum Euclidean length out of an
infinity number of solutions.
• If A has less than full column rank (over-determined system of
equations), LSQ returns the "solution" with the minimum residual value
e = A⋅x – b. The system of equations may not have a solution,
therefore, the value returned is not a real solution to the system, just
the one with the smallest residual.
Function LSQ takes as input vector b and matrix A, in that order. Function
LSQ can be found in Function catalog (‚N). Next, we use function LSQ
to repeat the solutions found earlier with the numerical solver:
Square system
Consider the system
with
2 3
A 1 3
2 2
The solution using LSQ is shown next:
2x + 3x –5x = 13,
1 2 3
x – 3x + 8x = -13,
1 2 3
2x – 2x + 4x = -6,
1 2 3
5
x
1
8 , x ,
x and
2
4
x
3
13
b 13 .
6
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