HP 48g Graphing Calculator - Manual (Page 218)

18
3. Enter the array of constants in the Bs field.
4. Move the highlight (if necessary) to the if“ field and press S
The result array (with the same dimensions as the constants arra}^
B) is displayed in the xs field and a labeled copy placed on the
stack.
5. Optional: Press E D I T to view the result in the MatrixWriter.
The Linear System Solver will return a result array for anj^ of the
following systems:
■ Exactly-Deterniiiied Systems. The number of equations equals the
number of independent variables in the system. The result returned
will be exact (to within the limits of precision of the HP 48), as long
as the coefficient matrix is not ill-conditioned (see “Ill-Conditioned
and Singular Matrices” on page 14-16).
B
Over-Determined Systems. The number of equations is greater than
the number of variables in the system. There is usually no exact
solution to over-determined systems so the least-squares solution is
returned.
m
Under-Determined Systems. The number of equations is smaller
than the number of independent variables in the system. There are
usually an infinite number of solutions to under-determined systems
so the one with the minimum Euclidean norm is returned.
Be sure to pay attention to the nature of the linear system you are
solving because it will influence how you should interpret the result
array. In some cases, you will want to test for ill-conditioning (see
page 14-16) before accepting even an exact solution as a “true”
solution.
Another approach to testing the validity of an answer is to find the
residual of the solution (A-X — B). Accurate solutions have residuals
close to zero.
To find the residual ( A - X - B )
1. Make sure the computed solution array is on stack level 1, and
press ( enter ) to duplicate it.
2. Enter the constants array (B) on the stack.
3. Enter the matrix of coefficients (A).
4. Press i^f STACK) F
1
.
5. Press SOLVE) :E
solution.
to move the solution array back to level
to compute the residual of the
18-12 Solving Equations