156 Section 12: Calculating with Matrices
Solving the Equation AX = B
The ÷ function is useful for solving matrix
equations of the form AX = B, where A is the
coefficient matrix, B is the constant matrix,
and X is the solution matrix. The descriptor
of the constant matrix B should be entered in
the Y-register and the descriptor of the
coefficient matrix A should be entered in the X-register. Pressing ÷ then
calculates the solution X = A
−1
B.
*
Remember that the ÷ function replaces the coefficient matrix by its LU
decomposition and that this matrix must not be specified as the result
matrix. Furthermore, using ÷ rather than ⁄ and * gives a solution
faster and with improved accuracy.
At the beginning of this section, you found the solution for a system of
linear equations in which the constant matrix and the solution matrix each
had one column. The following example illustrates that you can use the
HP 15c to find solutions for more than one set of constants—that is, for a
constant matrix and solution matrix with more than one column.
Example: Looking at his receipts for his
last three deliveries of cabbage and
broccoli, Silas Farmer sees the following
summary.
* If A is a singular matrix (that is, one that doesn’t have an inverse), then the HP 15c
modifies the LU form of A by an amount that is usually small compared to round-off
error. The calculated solution corresponds to that for a nonsingular coefficient matrix
close to the original, singular matrix.
Y
constant
matrix
X
coefficient
matrix
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