Hp 48g Graphing Calculator Bedienungsanleitung PDF herunterladen (Seite 179)

100

101

To calculate the “best” solution to any system of linear equations:

B1. 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 SOLVE 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 MhTR LSQ to calculate the “least-squares

solution” (X) that minimizes the residual (AX—B) (the minimized

Euclidean norm of the columns).

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:

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.

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

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