Derive for Windows, Version 4.10

Algebraic expressions in Derive 4 for Windows must be “authored” before operators
can be applied to them. This is easy to do: simply click on Author
on the menu bar, then click on Expression and type in the desired expression.
Alternatively, you can use the icon on the toolbar corresponding to the Author,
Expression commands. In fact, the toolbar contains shortcuts for many of the
most frequently used commands.

Derive 4 for Windows numbers each line of input and output as it is created
on the screen. The first line is referred to as “#1,” the second as “#2,” and so
on. The line numbering system in Derive 4 for Windows makes it easy to refer
to any previously created expression, as you will observe in the accompanying
figures.

At any given time in Derive 4 for Windows, at least one line or part of a line
is highlighted. You can change the highlighted area by using the arrow keys to
scroll up or down. Some commands, such as Simplify, are designed to apply to
the currently highlighted expression. In Derive 4 for Windows the most recent
output line is highlighted by default, which makes it convenient to simplify the
most recently computed expression. For example, if line #6 contains a dot
product such as [2, −3, 4] · [−1, 0, −2], and if this dot product is highlighted on
the screen, then clicking on Simplify and then on Basic produces a new line
(#7) containing the dot product −10.

Input of Vectors and Matrices; Fundamental Operations

To enter a vector or matrix, simply click on Author, and then on Vector or
Matrix. After indicating the dimension(s) of the vector or matrix, a template
of the correct size will form, which you fill in with the desired vector or matrix
entries. Use the Tab key to move from entry to entry.

Use the “+” and “−” keys between vectors or matrices for addition and
subtraction , respectively. Place a scalar before a vector or matrix to perform
scalar multiplication . Use a “.” (period) between vectors to perform dot product,
and between matrices to perform matrix multiplication. Use the “ ‘ ” (left
apostrophe) symbol after a matrix to calculate its transpose. The “^” symbol
is used to find powers of a ( square ) matrix. In particular, use “^(−1)” to
find the inverse of a (square) matrix. To convert fractions to decimals, use
the Approximate command, and specify the desired number of significant digits
displayed. These operations are illustrated in Figures D.7 and D.8.

Figure D.7: Derive 4 for Windows session: vectors; fundamental vector operations

Input	Output
Author, Matrix,3,4, OK, 4,Tab,-1,Tab,6,Tab,-2,Tab, -3,Tab,2,Tab,-3,Tab,2,Tab, -6,Tab,8,Tab,1,Tab,3,OK
Author,Matrix,4,3,OK,2,Tab,-3,(etc.)
Author, Expression,#5-2(#6‘),Simplify
Author, Expression,#5.#6,Simplify
Author, Expression,#8^(-1),Simplify
Simplify,Approximate,4,Approximate

Figure D.8: Derive 4 for Windows session: matrices; fundamental matrix operations

Solving a Linear System; Gauss-Jordan Row Reduction Method

You can solve a linear system directly using the Solve command. Click on
Solve and then System, and then indicate the number of equations to be solved .

A template will appear, into which you type each equation in turn. Under the
template, indicate the variables to be solved for. If the system has no solution,
the result “[ ]” will appear. If the system has more than one solution, each
independent variable will be represented with a differently numbered “@” symbol,
and the dependent variables will be expressed in terms of the independent
ones.

You can also solve a system using the row_reduce function. This function
computes the reduced row echelon form of a (possibly augmented) matrix. The
matrix on output line #12 below is the augmented matrix for a linear system
with an infinite solution set.

In Figure D.9, the same linear system is solved using both Solve and
row_reduce. You should verify that the general solution set obtained from
either method is equivalent to {(−3c+4, 2c +5, c, −2)}.

Input	Output
Solve,System,4,OK,3x+y+7z+2w =13,Tab,2x-4y+14z-w=-10, Tab,5x+11y-7z+8w=59,Tab, 2x+5y-4z-3w=39,Tab (x, y, z, w are highlighted), Simplify
Author,Matrix,4,5,OK,3,Tab,(etc.)
Author, Expression, row_reduce(#12), Simplify

Figure D.9: Derive 4 for Windows session: solution of a linear system; row reduction