156 Section 12: Calculating with MatricesSolving the Equation AX = B
The ÷function is useful for solving

 

 

matrix equations of the form AX = B,

Y

constant matrix

where A is the coefficient matrix, B is

 

 

X

coefficient

the constant matrix, and X is the

matrix

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-1B.*

 

 

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.