HP 39G

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276

TRACE

See User’s manual

TRN(matrix)

This function returns the transpose of an n x m matrix.

For example, if

23

112

04

M





=

−







then TRN(M1) would return

210

324









−





.

Table of Contents

Default Chapter2
- Table of Contents2
Introduction12
How to Use this Manual13
- Early High School13
- Pre-Calculus14
- Calculus14
Where's the on Button15
Some Keyboard Examples16
Keys & Notation Conventions17
- Some Essential Keys17
- The SHIFT Key17
- The ALPHA Key18
- The Screen Keys18
- Pop-Up Menus & Short-Cuts18
Everything Revolves Around Aplets21
- Some Typical Aplet Views22
The HOME View25
- What Is the HOME View25
- Exploring the Keyboard26
- Angle and Numeric Settings35
- Memory Management37
- Fractions on the Hp 39G40
  - Pitfalls to Watch for42
- The HOME History43
- Storing and Retrieving Memories45
- Referring to Other Aplets from the HOME View46
- An Introduction to the MATH Menu47
- Resetting the Calculator48
- Summary50
The Function Aplet51
- Choose the Aplet51
- The SYMB View52
- The Xtθ Button52
- Ing Your Function52
- The NUM View53
- The PLOT View53
- Auto Scale54
- The PLOT SETUP View55
- The Default Axis Settings57
- The Bar57
  - The MENU Toggle57
- The Menu Bar Functions58
- The FCN Menu63
Tips & Tricks - Function69
- Finding a Suitable Set of Axes69
- Composite Functions71
- Using Functions in the HOME View72
- Differentiating73
- Circular Functions74
- Trig Functions76
- Retaining Calculated Values77
- The NUM View Revisited77
- Zoom78
- Function80
- Integration: the Algebraic Indefinite Integral81
- The Hp 40G Computer Algebra System82
- Integration: the Definite Integral Using PLOT Variables83
- Piecewise Defined Functions85
- Nice' Scales86
- Use of Brackets in Functions87
- Problems When Evaluating Limits88
- Gradient at a Point90
- Finding and Accessing Polynomial Roots91
The VIEWS Menu92
- Plot-Detail93
- Plot-Table94
- Overlay Plot95
- Auto Scale96
- Decimal, Integer & Trig97
- Downloaded Aplets from the Internet99
  - Curve Areas99
  - Linear Programming99
The Parametric Aplet100
- Choose Xrng, Yrng & Trng100
- The Effect of Trng101
- Tstep Controls Smoothness101
Tips & Tricks - Parametric Equations103
- Fun and Games103
  - Example 1103
  - Example 2103
- Vectors104
  - Example 1104
  - Example 2105
The Polar Aplet106
- Choose Xrng, Yrng & Θrng106
- Θstep and Smoothness106
- Changing the Default for Θstep106
- Circular Circles106
The Sequence Aplet107
- Recursive or Non-Recursive107
- First, Second & General Terms107
- Convenient Screen Keys Provided108
Tips & Tricks - Sequences & Series110
- Defining a Generalized GP and the Sum to N Terms110
- Solving Sequence Problems110
- Modeling Loans112
The Solve Aplet113
- Equations Vs. Expressions113
- Entering the Equation113
- Solving for a Missing Value114
- The INFO Report114
- Multiple Solutions and the Initial Guess115
- Graphing in Solve116
- Transferring Approximate Solutions116
- Referring to Functions from Other Aplets117
- A Detailed Explanation of PLOT in Solve118
- The Meaning of Messages120
Tips & Tricks - Solve121
- Easy Problems121
- Harder Problems121
The Stats Aplet - Univariate Data122
- Uni Vs. Bi-Variate Data122
- Clearing Data122
- Sorting Data123
- The STATS Key123
- Functions of Columns124
- Registering Columns as 'In Use124
- Working with Frequency Tables125
- Auto Scale125
- Plot Setup Options126
- Box and Whisker Graphs126
- The Effect of Hrng127
- Grouped Data & Hwidth127
Tips & Tricks - Univariate Data129
- New Columns as Functions of Old129
- Simulating Dice129
- Simulating Random Variables130
The Stats Aplet - Bivariate Data132
- Uni Vs. Bi-Variate Data132
- Clearing Data132
- Entering Data as Ordered Pairs133
- Adjusting the Symbols Used to Plot Points133
- The Cursor133
- Sorting Paired Columns134
- Specifying the Fit Model134
- Multiple Data Sets134
- Choosing from Available Fit Models135
- The User Defined Model135
- Connected Data136
- Two Variable Statistics137
- Showing the Line of Best Fit138
- Predicting Using PREDY140
- Predicting Using the PLOT View140
- Relerr as a Measure of Non-Linear Fit141
Tips & Tricks - Bivariate Data143
- New Columns as Functions of Old143
- Using Values from in Calculations143
- Obtaining Coefficients from the Fit Model145
- Finding Fit Coefficients145
- Correct Interpretation of the PREDX Function146
- Assigning Rank Orders to Sets of Data147
- Using Stats to Find Equations from Point Data148
The Inference Aplet150
- Using the Chi2 Test on a Frequency Table150
- Hypothesis Test: T-Test 1-Μ151
- Confidence Interval: T-Int 1-Μ153
- Hypothesis Test: T-Test Μ154
- Hypothesis Test: Z-Test 1-Μ156
Tips & Tricks - Inference158
- Importing from a Frequency Table158
The Finance Aplet160
- Parameters160
- Straightforward Compound Interest161
- Annuity162
- Loan Calculations162
- Amortization163
The Quad Explorer Teaching Aplet164
- Objectives164
- Choosing the Level164
- GRAPH Mode164
- SYMB Mode165
- Self Test Mode166
The Trig Explorer Teaching Aplet167
- Objectives167
- SIN Vs. COS167
- SYMB Vs. GRPH Mode167
Using Matrices on the Hp 39G170
- The MATRIX Catalog170
- Matrix Calculations in the HOME View171
- Solving a System of Equations172
- Finding an Inverse Matrix174
- The Dot Product175
Using Lists on the Hp 39G176
- The List Variables176
- Operations on Lists176
- Statistical Columns as Lists176
- List Functions177
- Editing a List177
- Operations on Elements177
Using the Notepad Catalog178
- Aplet Notes Vs. Independent Notes178
- Independent Notes and the Notepad Catalog179
  - Transferring Notes Using IR180
  - Editing Software180
- Software181
  - For the Hp 38G, Hp 39G & Hp 40G181
  - For the Hp 39G181
- Creating a Note182
Using the Aplet Sketchpad184
- Adding Text to a Sketch184
- The DRAW Menu185
Using, Copying & Creating Aplets189
- Creating a Copy of a Standard Aplet190
  - Copying and Adding to the Function Aplet190
  - Copying and Adding to the Stats Aplet191
- Some Examples of Saved Aplets192
- Copying from Hp 39G+ to Hp 39G+ Via the Infra-Red Link197
- Downloading Aplets from the Internet200
Programming the Hp 39G212
- The Design Process212
- An Overview212
- Choosing the Parent Aplet212
- Naming Conventions213
- Planning the VIEWS Menu214
- The SETVIEWS Command214
- Special Entries in the SETVIEWS Command216
- The 'Start' Entry217
- Example Aplet #1217
- Example Aplet #2222
- Example Aplet #3224
- Example Aplet #4226
Programming Commands233
- The Aplet Commands233
- The Branch Commands234
- The Drawing Commands235
- The Graphics Commands237
- The Loop Commands237
- The Matrix Commands238
  - Editmat238
  - Redim238
- The Print Commands239
- The Prompt Commands240
The MATH Menu Functions243
- The 'Real' Group of Functions246
- The 'Stat-Two' Group of Functions254
  - Predy254
  - Predx254
- The 'Symbolic' Group of Functions255
- The 'Tests' Group of Functions259
- The 'Trigonometric' & 'Hyperbolic' Groups of Functions259
- The 'Calculus' Group of Functions261
- The 'Complex' Group of Functions262
- The 'List' Group of Functions265
- The 'Loop' Group of Functions269
- The 'Matrix' Group of Functions271
- The 'Polynomial' Group of Functions277
- The 'Probability' Group of Functions280
Appendix A: Worked Examples284
- Finding the Intercepts of a Quadratic284
- Finding Complex Solutions to a Complex Equation285
  - Method 1 - Using the QUAD Function285
  - Method 2 - Using POLYROOT285
- Finding Critical Points and Graphing a Polynomial286
- Solving Simultaneous Equations288
- Expanding Polynomials290
- Exponential Growth291
- Solution of Matrix Equations293
- Inconsistent Systems of Equations294
  - Using the RREF Function294
- Finding Complex Roots295
- Analyzing Vector Motion and Collisions296
- Circular Motion and the Dot Product297
- Inference Testing Using the Chi 2 Test299
Appendix B: Teaching Calculus with an Hp 39G301
- Investigating y X = N for N an Integer301
- Investigating y X= for N an Integer302
- Domains and Composite Functions302
- Gradient at a Point303
- Gradient Function304
- The Chain Rule305
- Optimization305
- Area under Curves306
- Fields of Slopes and Curve Families306
- Inequalities307
- Rectilinear Motion307
- Limits307
- Piecewise Defined Functions308
- Sequences and Series308
- Transformations of Graphs309
Appendix C: the Hp 40G & Its CAS310
- Introduction310
  - What Is a CAS310
  - What Is the Difference between the Hp 39G, Hp 40G & Hp 39G312
- Using the CAS313
- Using Functions in the CAS321
- On-Line Help328
- Configuring the CAS329
- Tips & Tricks - CAS330

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