Using the HP48G Series Calculator to solve Systems of Linear Equations.

In order to solve a set of linear equations using the HP48G series calculator, you must first organize your equations in a systematic form to enter the various coefficients. Each equation must include a coefficient for each variable, even if that coefficient is zero.

First, collect terms in each equation, then write the equations with the variables to the left of the "=" in the same order from left to right, and the constant (which may also be zero) on the right of the "=". (See example below.) The coefficients by each variable will be entered as an N X N array (where there are N variables), and the constants will be entered as an N element column matrix.

EXAMPLE:

After collecting terms with a set of mesh equations, you have the following three equations in three unknowns:

10K ia + 11K ib -  3K ic = 5
  7 ia +   8 ib +   0 ic = 0
  0 ia - 22K ib + 15K ic = 9

Note that each equation has been organized with the three variables i_a, i_b, and i_c in the same order on the left of the "=" and the constants on the right of the "=". Also note that each variable is present, even if its coefficient in a given equation is zero.

Now, the coefficients of the variables are placed in a matrix in the same order that they appear in the equations:

10K   11K   -3K
 7     8     0
 0   -22K   15K

and the constants on the right are placed in a single column matrix:

5
0
9

Press right-shift SOLVE (7) which will open a menu. Select "Solve Linear Sys..." using the cursor keys and press the OK menu button. You are now in the solver for simultaneous linear equations. The window title should read "SOLVE SYSTEM A^.X=B". A and B are the two matrices above.

The first line should have "A:" and the area next to it should be highlighted (dark). If it is not, use the cursor keys to highlight the space to the right of "A:".

To enter matrix A, press the EDIT menu key and the matrix entry screen will appear with the top left element highlighted. There are various ways to enter the matrix, but I will choose to enter it by columns. Find the menu item labelled . If this label does not have a small square next to it, press the button directly under it and the square should appear . This tells the calculator that we will be entering the data by columns.

Now enter the first column:

10 <EEX> 3 <ENTER>

7 <ENTER>

0 <ENTER>

At this point, we need to tell the calculator that we have reached the last row and wish to begin the next column. Press the right cursor key and the highlighted element will switch to the top row of the second column. Enter the next column:

11 <EEX> 3 <ENTER>

8 <ENTER>

22 <+/-> <EEX> 3 <ENTER>

Note that when you have finished this column, the highlighted element automatically moves to the top of the third column, you do not have to retell it how many rows there are.

Enter the last column:

3 <+/-> <EEX> 3 <ENTER>

0 <ENTER>

15 <EEX> 3 <ENTER>

Now the top row of the fourth column is selected and the calculator awaits entry of column four. Since there is no column four, you must tell it the matrix is finished: press <ENTER> one more time.

The calculator will return to the "SOLVE SYSTEM" screen, and the first few elements of the matrix should be visible in the row next to A:

Now we must enter matrix B. This is very similar, except there is only a single column. Use the down cursor key to select the next row (labelled B:), press the EDIT menu button, again make sure is selected (small square next to the label) then type:

5 <ENTER>

0 <ENTER>

9 <ENTER>

<ENTER>

Press the down cursor key to highlight the next row (labelled X:) and press the SOLVE menu button. You should see numbers appear by X: after a brief delay. To see all of the solutions, press the EDIT menu button. This takes you back to the matrix screen. Usually, the numbers are too large to display in the limited space available, but the highlighted value is shown at the bottom of the screen. You can view each value in turn by using the cursor keys to move up or down. The solutions from top to bottom are in the same order as the variables from left to right in the original equations. Thus, rounded to four significant figures, we have:

i_a = 1.6095 mA

i_b = -1.4083 mA

i_c = -1.4655 mA

These values are also available on level one of the stack when you exit the Linear System Solver.