HP 48g Graphing Calculator - Manual (Page 179)

To calculate the “best” solution to any system of linear equations:
B 1. Press CTfsoivrimm OK to open the SOLVE SYS i EM fl
input form.
2. Enter the matrix of coefficients into field fl:.
3. Enter the array (vector or matrix) of constants into field B: .
4. Press S O L V E to calculate the “best” solution and display it in
the K field. If the system being solved is exactly-determined, the
solution is a 12-digit approximation of the exact solution; if it is
over- or under-determined, then the solution is the minimum norm
least-squares solution (to 12 digits).
To estimate the solution to an over-determined system of linear
equations:
1. Enter the array (vector or matrix) of constants onto the stack.
2. Enter the matrix of coefficients. It will typically have more rows
than columns.
3. Press
[MTH 1
M h T R L S Q to calculate the “least-squares
solution” (X) that minimizes the residual (AX—B) (the minimized
Euclidean norm of the columns).
14
To estimate the solution to an under-determined system of linear
equations:
1. Enter the array (vector or matrix) of constants onto the stack.
2. Enter the matrix of coefficients. It will typically have more columns
than rows.
3. Press
fMTHl
MflTR LSQ to calculate the one “least-squares
solution” (X) of many possible least-square solutions that has the
smallest Frobenius norm.
To solve an exactly-determined system of linear equations:
3.
Enter the vector of constants onto the stack.
Enter the square matrix of coefficients. The number of columns
(“variables”) in the matrix must equal the number of elements in
the vector.
Press ©• The result will be a solution vector of the same size
as the constants vector. Note that array division can produce
erroneous results if you are using ill-conditioned matrices. See
“Ill-Conditioned and Singular Matrices” below.
Matrices and Linear Algebra 14-15