<Text-field style="Heading 1" layout="Heading 1">Starting a New Worksheet: Do This First!</Text-field>

Maple Worksheets: Getting Started

Tips for getting started:

Maple commands and variables are case sensitive and order of command execution is important!

Commands can be executed individually by pressing "Enter" at each command.

Organize executable commands by placing them after Maple prompts ("[>").

Use Shift+Enter to create a new line at the same prompt without executing the command.

Use the "!!!" button to execute all commands in your worksheet in order, "!" will execute only selected commands.

You can insert plain text that is not executed as a command, and you can format this text as you would with a word processor.

You can press Esc or Ctrl+Space to pull up a list of symbols and commands that complete what you just typed.

<Text-field style="Heading 1" layout="Heading 1">Starting a New Worksheet: Do This First!</Text-field>

Clearing Variables

At the start of every worksheet, it's a good idea to clear all variables using "restart," otherwise you may get unexpected results!

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Loading Additional Packages

You may also want to use some additional Maple packages, load these using "with."

Some tools for creating various plots

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Packages useful for Linear Algebra (colon hides output)

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Packages for working with Differential Equations

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JSFH

<Text-field style="Heading 1" layout="Heading 1">Basic Command Syntax</Text-field>

Comments

You can create a comment that will not be executed by inserting plain text between your Maple prompts (as I have been doing.) You can also insert a comment using "#"

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Variables

Values are assigned to variables with ":=" not with "=", which is reserved for equations. Notice how Maple handles LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the following:

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This can be useful if we want to assign an equation to a variable name

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You need to be very careful when defining variables. If you are having problems executing commands in your worksheet, check your variable assignments!

Terminating Statements

Semicolons and colons are used as statement separators in Maple, use these to terminate your statements. Use a semicolon at the end of each statement to display the output once the command is executed. A colon at the end of the statement will execute the command, but will not display the output.

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<Text-field style="Heading 1" layout="Heading 1">Using and Defining Functions and Procedures</Text-field>

Maple has many procedures defined to do various tasks. Procedures will require that you specify certain parameters (some may be optional) which are explained in Maple help, usually along with some examples.

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Functions

Mathematical functions are treated as a special type of procedure in Maple, using arrow notation ("->").

For instance, to define 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 as a function:

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

Now we can evaluate 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at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGNEY0RjQ=:

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

Procedures

Procedures can extend to more than just mathematical functions, the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYjUSFGJy9GM1Enbm9ybWFsRidGPUY9 procedure used above can take an expression or list as a parameter. Defining our function above as a procedure is slightly more complicated, since we need to specify the input type:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUkjbWlHRiQ2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GUy1GNjYvUSVwcm9jRicvJSVib2xkR0YxL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0ZlbkY7Rj5GQEZCRkRGRkZIRlJGVC1JKG1mZW5jZWRHRiQ2JC1GIzYsLUYsNiVRInhGJ0YvRjJGTy1GNjYtUS0mUHJvcG9ydGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGSkZNRk8tRiw2JVEobnVtZXJpY0YnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRlIvRk5RLDAuMzMzMzMzM2VtRidGTy1GLDYlUSJ5RidGL0YyRmBvRmNvRjktRiw2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGUy8lJmRlcHRoR0ZncC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0ZPRk9GTy1JJW1zdXBHRiQ2JUZdby1GIzYjLUkjbW5HRiQ2JFEiMkYnRjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GX3ItRmBxNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGUi9GTlEsMC4xMTExMTExZW1GJy1GIzYjRlxwRmhxRl9wLUZjcDYmRmVwRmhwRmpwL0ZdcVElYXV0b0YnRmJwLUY2Ni9RJGVuZEYnRlhGWkZmbkY7Rj5GQEZCRkRGRkZIRlJGVC1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==

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

JSFH

<Text-field style="Heading 1" layout="Heading 1">Palettes and Right Click Context Menus</Text-field>

Palettes

Maple supports many operators, symbols and expressions. The most common of these are available in palettes, so that you can select them without knowing the correct syntax for the procedure and read them in a more familiar format.

The following statements use the Expression palette and the equivalent procedure:

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

Right Click

Right clicking on an expression will give you a context menu to perform operations without knowing the correct procedure. Notice that some of the following operations result in complex procedures!

Right clicking on the following expression allows us to evaluate for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=:

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

or solve for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

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JSFH

or differentiate implicitly with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=:

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

or plot:

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

More Examples

From here on, I will assume some familiarity with calculus and linear algebra topics. If something looks unfamiliar, try searching for it in help!

<Text-field style="Heading 1" layout="Heading 1">Calculus</Text-field>

We'll work with the following functions for these problems:

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

Limits

To evaluate limits we can use the expression palette:

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

or we can use the equivalent command limit(function, point, direction):

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmbGltaXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnLUYjNiMtRiw2JVEieEYnRi9GMi8lLmxpbmV0aGlja25lc3NHRkAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTC8lKWJldmVsbGVkR1EmZmFsc2VGJy1JI21vR0YkNi1RIixGJ0ZBLyUmZmVuY2VHRlEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGUS8lKnN5bW1ldHJpY0dGUS8lKGxhcmdlb3BHRlEvJS5tb3ZhYmxlbGltaXRzR0ZRLyUnYWNjZW50R0ZRLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGRS1GUzYtUSI9RidGQUZWL0ZZRlFGWkZmbkZobkZqbkZcby9GX29RLDAuMjc3Nzc3OGVtRicvRmJvRmlvLUYsNiVRKWluZmluaXR5RidGL0YyRkEtRlM2LVEiO0YnRkFGVkZYRlpGZm5GaG5Gam5GXG9GXm9Gam8=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmbGltaXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnLUYjNiMtRiw2JVEieEYnRi9GMi8lLmxpbmV0aGlja25lc3NHRkAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTC8lKWJldmVsbGVkR1EmZmFsc2VGJy1JI21vR0YkNi1RIixGJ0ZBLyUmZmVuY2VHRlEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGUS8lKnN5bW1ldHJpY0dGUS8lKGxhcmdlb3BHRlEvJS5tb3ZhYmxlbGltaXRzR0ZRLyUnYWNjZW50R0ZRLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGRS1GUzYtUSI9RidGQUZWL0ZZRlFGWkZmbkZobkZqbkZcby9GX29RLDAuMjc3Nzc3OGVtRicvRmJvRmlvLUY+NiRRIjBGJ0ZBRkEtRlM2LVEiO0YnRkFGVkZYRlpGZm5GaG5Gam5GXG9GXm9Gam8=

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

Differentiation

Maple has several procedures for differentiation, the expression palette contains some familiar notation:

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

These are equivalent to the diff(expression, variables) command:

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Another procedure that can be used is the differential operator D[argument indices](function)(evaulation point). This is slightly different from the diff() operator, as it can evaluate derivatives at a point, but cannot handle expressions that are not functions:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJmRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMi1GNjYkLUYjNiMtRiw2JVEieEYnRj1GP0YyLUkjbW9HRiQ2LVEiO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJmRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMi1GNjYkLUYjNiMtSSNtbkdGJDYkUSIwRidGMkYyLUkjbW9HRiQ2LVEiO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw==

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Integration

Integration is also easily accomplished using the expression palette:

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVErJkludGVncmFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZERistSSNtaUdGJDYlUSJnRicvJSdpdGFsaWNHRjkvRjBRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRkg2JVEieEYnRktGTS1GLDYtUSIsRidGL0YyL0Y2RjkvRjhGNEY6L0Y9RjRGPkZARkIvRkZRLDAuMzMzMzMzM2VtRictRkg2JVEieUYnRktGTUYvLUYsNi1RIn5GJ0YvRjJGNUZlbkY6RmZuRj5GQEZCRkUtRiw2LVEwJkRpZmZlcmVudGlhbEQ7RidGLy9GM1EmdW5zZXRGJy9GNkZjby9GOEZjby9GO0Zjby9GPUZjby9GP0Zjby9GQUZjb0ZCRkVGVEZcb0Zfb0Zpbi1GLDYtUSI7RidGL0YyRlpGZW5GOkZmbkY+RkBGQi9GRlEsMC4yNzc3Nzc4ZW1GJw==

Of course there is an equivalent command, int(expression, variables):

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkaW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEiZkYnRi9GMi1GNjYkLUYjNiMtRiw2JVEieEYnRi9GMi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGRC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZMLyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GRzYtUSJ+RidGREZKL0ZORkxGT0ZRRlNGVUZXRlkvRmduRmVuRkFGRC1GRzYtUSI7RidGREZKRk1GT0ZRRlNGVUZXRlkvRmduUSwwLjI3Nzc3NzhlbUYn

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Additional Topics

Maple also has commands for many other specific calculus topics, here are a few that might be useful (look up syntax in the help menu!):

taylor outputs a Taylor series expansion

dsolve is a solver for ordinary differential equations

inttrans[laplace] performs a Laplace transform

BesselI, BesselJ, BesselK and BesselY can be used to call the various Bessel functions

LegendreP and LegendreQ can be used to call the Legendre functions

JSFH

<Text-field style="Heading 1" layout="Heading 1">Linear Algebra</Text-field>

Remember to load the LinearAlgebra package! Notice all of the different commands this will allow us to use, many of which can be very tedious to perform by hand for large matrices:

QyQtSSV3aXRoRzYiNiNJLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUiIiI=

Matrices

We won't get very far before we need to input a matrix of some sort. We can use the Matrix() command to generate some matrices quickly, but it is often simpler to use the Matrix palette. Double click on a large matrix to see and edit its entries:

QyQ+SSJBRzYiLUknTWF0cml4R0YlNiUiIiNGKTckNyQiIiJGKTckRikiIiUhIiI=

QyQ+SSJCRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiKi8pKj5fIiEiIg==

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QyQ+SSNDMkc2Ii1JLVJhbmRvbU1hdHJpeEdGJTYlIiQrIi9JKmdlbmVyYXRvckdGJTsiIiEiIiovSS5vdXRwdXRvcHRpb25zR0YlNyMvSSZzaGFwZUdGJUkqaGVybWl0aWFuR0YlIiIi

Vectors

Vectors can be defined using angled brackets (< >):

Qyg+SSN2MUc2Ii1JJDwsPkdGJTYlIiIiISIiRilGKT5JI3YyR0YlLUYnNiVGKUYpRilGKT5JI3YzR0YlLUYnNiUiIiMiIiFGKUYp

Matrix Arithmetic

Matrices can be easily added and subtracted, but there are two kinds of multiplication. We can multiply a matrix by a scalar using *, the product of two matrices is not commutative and uses a period:

QyQsJkkiQUc2IiIiIkkiQkdGJUYmRiY=

QyQsJkkiQUc2IiIiIkkiQkdGJSEiIkYm

QyQsJEkiQUc2IiIiJiIiIg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRIkJGJ0YvRjItRjY2LVEiO0YnRjlGOy9GP0YxRkBGQkZERkZGSEZKL0ZOUSwwLjI3Nzc3NzhlbUYn

QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJIkJHRikiIiI=

QyQtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkJHRilJIkFHRikiIiI=

Useful Functions

We can use commands to manipulate matrices quickly (see the output of with(LinearAlgebra) above). Here are a few examples:

QyQtSSxEZXRlcm1pbmFudEc2IjYjSSJBR0YlIiIi

QyQtSSxFaWdlbnZhbHVlc0c2IjYjSSJBR0YlIiIi

QyQtSS1FaWdlbnZlY3RvcnNHNiI2I0kiQUdGJSIiIg==

QyQtSTBMVURlY29tcG9zaXRpb25HNiI2I0kiQUdGJSIiIg==

QyQtSTBRUkRlY29tcG9zaXRpb25HNiI2I0kiQUdGJSIiIg==

QyQtSSxHcmFtU2NobWlkdEc2IjYjPCVJI3YxR0YlSSN2MkdGJUkjdjNHRiUiIiI=

QyQtSSxHcmFtU2NobWlkdEc2IjYkPCVJI3YxR0YlSSN2MkdGJUkjdjNHRiVJK25vcm1hbGl6ZWRHRiUiIiI=

Santa Barbara City College Mathematics Department, Allison Chapin 2010

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=