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## HP 50g Graphing Calculator - Solving Linear Systems of Equations using Matrices## The Numeric SolverThe HP 50g has a numeric solver that can find the solutions to many different types of problems. It is invoked by pressing the
ORANGE shift key followed by the
key, or
.
When pressed, the CHOOSE box below is displayed: Figure 1: Displaying the options in the numeric solver The first choice allows for the solution of an equation containing a number of unknowns. The second choice solves differential
equation problems. The third choice solves for zeroes of a polynomial. The fourth choice to solve linear systems of equations is the
one of interest here. The fifth choice invokes the finance solver. The sixth choice begins the multiple equation solver. To select the
linear systems solver, press
. The 50g displays the following screen:
Figure 2: Selecting the linear systems solver There are three input areas on this form. The first area is labeled A: and is where the matrix containing the coefficients of the system
of linear equations are entered. The second area is labeled B: and is where the constants from the system of equations are entered.
The third area is where the values of the unknown variables X in the systems of linear equations are returned when a solution is
found. To enter the coefficients in a matrix, press
when the cursor is beside the area labeled A: and the MatrixWriter is
launched.
Figure 3: Entering the coefficients in a matrix In many ways, this screen works like any spreadsheet. Enter numbers and they will go in the highlighted cell. The menu labels at the
lower left corner of the screen,
and
, determine the direction the cursor moves after a data point has been entered, either
right to the next column or down to the next row. In this example, the selection is to move right after each data point has been
entered. This is indicated by the square present next to the
menu label. To change the way the cursor will move, press the
menu label for the direction desired and the square in the menu label will change accordingly. If a column is too small to show the
data entered, the
and
menu keys may be used to expand or shrink the area displayed for each column.
Enter the first coefficient from the first equation by keying in the numbers and pressing the
key. The cursor will move to the right
into the second column where the second coefficient should be keyed with the
key pressed to accept this value. At this point,
the cursor will be in column 3. If the system of linear equations being entered has more than two unknown variables, continue
entering the data until done. Use the
and
keys to move back to the first column and enter the coefficients from the second equation. Continue entering rows of data into the matrix until done. If at any time you notice a mistake in the data, use the arrow keys
to go back to the incorrect data value, key in the correction, press the
key to accept the change, and then use the arrow keys to
go back to where you were. After entering a matrix, the screen would look something like this:
Figure 4: The screen displays after entering a matrix To accept the data as input, press the
key and the matrix will be returned to the system of linear equations solver.
Figure 5: Displaying the linear equations solver To enter the constants for the linear equations, press the
key and press the menu label
above the
key. The
MatrixWriter will be brought up a second time to enter the constants.
NOTE: The constants are entered as a column of numbers
rather than a row. Enter the numbers the same way that the coefficients were entered.
Figure 6: Entering the constants for the linear equations When the
key is pressed, the constants are returned to the linear equation system solver in the B: area, as shown below.
Figure 7: Displaying the constants in the B: area To solve for the values of X that make the system of linear equations work, use the arrow keys to move down to the X: area. Press
the menu label
above the
key and the values of X
_{1} and X_{2} that solve the linear system are returned and displayed.Figure 8: Displaying the constants in the X: area The solution may be seen easier by pressing
above the
key to view the solution in the MatrixWriter. If the columns are
too small to see many significant figures, press the
menu label to make them wider.
Figure 9: Displaying the data by expanding the columns You may also exit to the stack and view the solutions on the first level. To exit to the stack from within the MatrixWriter, as we were
immediately above, press
and the display will show:
Figure 10: Displaying the solution ## Solving linear systems of equationsThere are many times when a problem is presented of the form: 5 X 4 X and the values of X ## Practice solving linear systems
## Example 1What are the values of X 5 X 4 X ## SolutionTo solve this linear system, use the numeric solver as shown. Figure 11: Entering the equation using the numeric solver Figure 12: Displaying the constants in the A: area Figure 13: Entering the second portion of the equation Figure 14: Displaying the values in the B: area Figure 15: Displaying the X1result Figure 16: Displaying the data by expanding the column Figure 17: Displaying the result ## AnswerThe value of X ## Example 2What are the values of X 3 X 1 X 4 X ## SolutionTo solve this linear system, use the numeric solver as shown. Figure 18: Entering the equation using the numeric solver Figure 19: Displaying the values in the B: area Figure 20: Displaying the X1 result Figure 21: Displaying the result ## AnswerThe value of X |

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