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# HP 50g Graphing Calculator - Working with Matrices

## The MatrixWriter form

The HP 50g contains a wonderful form built-in to facilitate the entry of matrices. This form is called the MatrixWriter, and it is the
ORANGE shifted function of the key. To start the MatrixWriter, press . The screen below is displayed to allow for the
entry of data into a matrix.

**Figure : MatrixWriter**

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 data value by keying in the numbers and pressing the key. The cursor will move to the right into the second
column where the second data value should be keyed with the key pressed to accept this value. At this point, the cursor will be
in column 3. If the matrix being entered has more than two columns of data, continue entering the data until done. Use the and
keys to move back to the first column and enter the second row of data (if any). 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 : Entering the matrix**

To accept the data as input, press the key and the matrix will be placed on the first level of the stack.

**Figure : First level of the stack**

## The Matrix.. part of the MTH (MATH) CHOOSE box

The Math menu is accessed from the WHITE shifted function of the key by pressing . When pressed, a CHOOSE
box is displayed with a number of choices allowing problems to be solved with different math functions on the HP 50g calculator.

**Figure : MATH MENU**

The first choice allows for calculations dealing with vectors. The second choice provides access to many functions for working with
matrices. The third choice allows for the manipulation of lists and for using lists to apply mathematical functions to a list of numbers,
all at the same time. The fourth function provides access to the hyperbolic trigonometric functions. The fifth selection provides a list
of many functions that can be applied to real numbers. The sixth choice displays functions dealing with numbers in different bases.
Choices seven through eleven are not displayed in the screen above, but deal with probability, fast fourier transformations, complex
numbers, constants and a choice dealing with several special functions. We are interested in the second choice for working with
matrices. To access that second-level CHOOSE box, either press to display the list of matrix functions.

**Figure : MATRIX MENU**

There are a large number of functions available to use on matrices. The practice problems will illustrate only a few of these.

## Practice solving problems involving matrices

### Example 1

What is the determinant of the matrix shown below? Assume RPN mode.

**Figure : RPN mode**

### Solution

To find the determinant, use the MatrixWriter to enter the matrix as shown.

The matrix should now be on the first level of the stack as shown above. The determinant function is found in
the MTH (MATH) CHOOSE box, in the MATRIX.. second-level CHOOSE box, in the NORMALIZE third-level
CHOOSE box as function number 8. If this function is used frequently, there are several ways to access it much
more quickly. A USER key assignment can be made (which is discussed in another of these training aids). The
function can be placed in a CUSTOM menu. The function can also be spelled out using the det
letter keys and pressing . The 50g is very flexible. The solution shown below will use the CHOOSE box
approach.

**Figure : CHOOSE box approach**

**Figure : Answer**

The determinant of the matrix is –2,432.

### Example 2

Transpose the matrix shown below and find the inverse of the transposed matrix. Assume Algebraic mode.

**Figure : Transposing the matrix**

### Solution

To transpose the matrix and find the inverse, use the MatrixWriter to enter the matrix as shown.

The matrix should now be on the first level of the stack as shown above. To transpose the matrix, use the TRAN
command, which is the 10th command of the NORMALIZE CHOOSE box (which makes it two below the DET
command used in the previous example).

**Figure : Using the TRAN command**

Since we are in algebraic mode for this example, the TRAN() command is copied to the command line and is
looking for a matrix to transpose as an argument to the function.

**Figure : Transposing an argument to the function**

Since the matrix is in the first level of the command stack, we can use to fill in the argument needed.

**Figure : First level of the command stack**

When is pressed, the transposed matrix is in the first level of the command stack.

**Figure : Transposed matrix**

Finding the inverse of a matrix can be done by pressing the key. In algebraic mode, this will place the
INV() function (which is how the reciprocal function is displayed as a text command) on the command line looking
for a matrix to serve as the argument for the function. Sine the transposed matrix is on the first level of the command
stack, to find the inverse of this transposed matrix, press:

The inverse is displayed as shown below (assuming EXACT mode):

**Figure : EXACT mode**

Since this matrix may scroll off the top of the screen, we can use the function (which is above the key)
from the menu to take a closer look at the solution. The arrow keys allow the view to be moved around on the
screen. If desired, press to see the matrix in a different format.

The inverse of the transposed matrix is shown below.

**Figure : Answer**

or as shown in the viewpoint:

**Figure : Text viewpoint**

### Example 3

What are the characteristic roots (or eigenvalues) of the matrix shown below? Assume RPN mode.

**Figure : RPN mode**

### Solution

To find the characteristic roots, use the MatrixWriter to enter the matrix as shown.

The matrix should now be on the first level of the stack as shown above. The eigenvalues function is found in
the MTH (MATH) CHOOSE box, in the MATRIX.. second-level CHOOSE box as function number 8.

**Figure : Using teh EGV command**

**Figure : Answer**

The characteristic roots or eigenvalues are –3 and –9.

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