HP 39g Graphing Calculator User's Guide Page 179
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Matrices 12-7
To multiply two
matrices
To multiply the two matrices M1 and M2 that you created for
the previous example, use the following keystrokes:
>$/3+$@M1>[@ >$/3+$@M2
>(17(5@
To multiply a matrix by a vector, enter the matrix first, then
the vector. The number of elements in the vector must equal
the number of columns in the matrix.
To divide by a
square matrix
For division of a matrix or a vector by a square matrix, the
number of rows of the dividend (or the number of elements, if
it is a vector) must equal the number of rows in the divisor.
This operation is not a mathematical division: it is a left–
multiplication by the inverse of the divisor. M1/M2 is
equivalent to M2
–1
* M1.
To divide the two matrices M1 and M2 that you created for the
previous example, use the following keystrokes:
>$/3+$@M1 >j@>$/3+$@M2
>(17(5@
To invert a matrix You can invert a square matrix in HOME by typing the matrix
(or its variable name) and pressing >6+,)7@x
–1
>(17(5@. Or you
can use the matrix INVERSE command. Enter
INVERSE(matrixname) in HOME and press >(17(5@.
To negate each
element
You can change the sign of each element in a matrix by
pressing >@ before the matrix name.
- USER’S GUIDE 1
- Contents 3
- 9 Inference aplet 5
- 12 Matrices 6
- 13 Lists 6
- 14 Notes and sketches 6
- 15 Programming 7
- 16 Extending aplets 7
- Manual conventions 9
- P-2 Preface 10
- Getting started 11
- The display 12
- The keyboard 13
- Aplet control keys 14
- >@) 15
- Shifted keystrokes 16
- Program 17
- 1-8 Getting started 18
- Input forms 19
- Mode settings 19
- 1-10 Getting started 20
- Aplets (E–lessons) 21
- displays a 23
- Trig Explorer 24
- Aplet library 25
- Aplet views 25
- 1-16 Getting started 26
- Aplet view configuration 27
- Mathematical calculations 28
- Example Calculate 29
- 1-20 Getting started 30
- Clearing 31
- 1-22 Getting started 32
- Storing a value 33
- Accessing the 33
- Using fractions 34
- Setting 35
- Fraction 36
- Converting 36
- Complex numbers 37
- Catalogs and editors 38
- HP 39G/40G 39
- Aplets and their views 41
- 2-2 Aplets and their views 42
- Evaluating expressions 43
- SYMB view 44
- About the Plot view 45
- Reset plot 46
- Zoom within a 48
- Aplets and their views 2-9 49
- 2-10 Aplets and their views 50
- Aplets and their views 2-11 51
- To set zoom 52
- VIEWS menu 53
- 2-14 Aplets and their views 54
- About the numeric view 55
- Reset numeric 56
- NUM view 57
- NUM), choose NUMTYPE: 58
- CLEAR) 58
- “Build Your Own” menu keys 59
- Example: plotting a circle 60
- Function aplet 61
- Plot the 62
- Function aplet 3-3 63
- 3-4 Function aplet 64
- Function aplet 3-5 65
- Display the 66
- Set up the 66
- Explore the 67
- 3-8 Function aplet 68
- Access FCN 69
- 3-10 Function aplet 70
- 1 >@ >(17(5@ 71
- Parametric aplet 73
- Set angle 74
- Polar aplet 77
- for and R1 78
- Sequence aplet 79
- Specify plot 80
- Solve aplet 83
- 7-2 Solve aplet 84
- Solve the 85
- ≈20 times 86
- Solve aplet’s NUM view keys 86
- Use an initial guess 87
- Interpreting results 88
- The Root 89
- Finder at work 89
- Plotting to find guesses 90
- SETUP-PLOT 91
- Using variables in equations 92
- Choose fit and 95
- Explore 95
- 8-4 Statistics aplet 96
- Statistics aplet 8-5 97
- CLEAR to 98
- Statistics aplet 8-7 99
- 8-8 Statistics aplet 100
- CLEAR is used the data 101
- SETUP-PLOT 102
- CLEAR. Select 102
- Sort data 103
- To choose the 103
- To define your 104
- Computed statistics 105
- Two-variable 106
- Plotting You can plot: 107
- Plot types 108
- Fitting a curve to 2VAR data 109
- SETUP-PLOT) sets most of the 110
- Trouble-shooting a plot 111
- Exploring the graph 112
- Calculating predicted values 113
- Inference aplet 115
- Open the 116
- Define the 117
- SETUP-NUM 118
- Plot test 119
- Statistics aplet 119
- Calculate 120
- Display 122
- Numeric view 122
- Display Plot 122
- Hypothesis tests 123
- Two–Sample Z–Test 124
- One–Proportion Z–Test 125
- Two–Proportion Z–Test 126
- One–Sample T–Test 127
- Two–Sample T–Test 128
- Inputs The inputs are: 129
- Results The results are: 129
- Confidence intervals 130
- Two–Sample Z–Interval 131
- One–Proportion Z–Interval 132
- Two–Proportion Z–Interval 133
- One–Sample T–Interval 134
- Two–Sample T–Interval 135
- Using mathematical functions 137
- To select a 138
- Function categories 138
- Math functions by category 139
- Keyboard functions 140
- Calculus functions 143
- Complex number functions 144
- Constants 145
- Hyperbolic trigonometry 145
- List functions 146
- Loop functions 147
- Matrix functions 147
- Polynomial functions 148
- Probability functions 149
- Real-number functions 151
- Statistics-Two 154
- Symbolic functions 155
- Test functions 156
- Trigonometry functions 157
- Symbolic calculations 158
- Finding derivatives 159
- To find 160
- Function aplet’s 160
- Symbolic view 160
- To find the 161
- Introduction 163
- Numeric 164
- Precision 164
- To store the 165
- The VARS menu 166
- To access an 170
- Memory Manager 171
- Matrices 173
- Creating and storing matrices 174
- To create a matrix 175
- Working with matrices 176
- MATRIX), highlight the 177
- Matrix arithmetic 178
- Matrices 12-7 179
- 12-8 Matrices 180
- Matrix functions and commands 181
- Argument conventions 182
- n orthogonal]] 183
- 12-12 Matrices 184
- Examples 185
- Reduced-Row 186
- Echelon Form 186
- Creating lists 187
- CLEAR Clears all lists 188
- Create a list in 189
- Displaying and editing lists 190
- To insert an 191
- To store one 191
- Deleting lists 192
- Transmitting lists 192
- 13-8 Lists 194
- Lists 13-9 195
- 13-10 Lists 196
- Lists 13-11 197
- Notes and sketches 199
- Note edit keys 200
- Aplet sketch view 201
- DRAW keys 202
- Notes and sketches 14-5 203
- The notepad 204
- Notepad Catalog keys 205
- NOTEPAD), open the note 206
- Programming 207
- Program catalog 208
- Program catalog keys 209
- Creating and editing programs 210
- CMDS to open the 211
- PROGRM to 211
- 15-6 Programming 212
- Using programs 213
- Working with programs 214
- About customizing an aplet 215
- Aplet naming convention 216
- Customizing an aplet example 216
- Configuring 217
- 15-12 Programming 218
- Programming 15-13 219
- Programming commands 220
- Programming 15-15 221
- Auto-run programs 222
- ProgramName 222
- ViewNumber 222
- Branch commands 223
- 15-18 Programming 224
- Drawing commands 225
- Graphic commands 226
- Programming 15-21 227
- Loop commands 228
- Matrix commands 229
- 15-24 Programming 230
- Print commands 231
- Prompt commands 231
- CMDS >@ *A, >6,1@ 232
- Programming 15-27 233
- 15-28 Programming 234
- Stat-One commands 235
- Stat-Two commands 235
- Plot-view variables 236
- Extremum 237
- Hmin/Hmax 237
- InvCross 238
- Nmin / Nmax 239
- Recenter 239
- S1mark–S5mark 239
- StatPlot 240
- Umin/Umax 240
- Tmin / Tmax 241
- Xmin / Xmax 242
- Ymin / Ymax 242
- Symbolic-view variables 243
- 15-38 Programming 244
- Numeric-view variables 245
- NumIndep 246
- NumStart 247
- Note variables 248
- Sketch variables 248
- Extending aplets 249
- Aplet Keys 250
- Extending aplets 16-3 251
- Resetting an aplet 252
- Sending and receiving aplets 253
- To sort the 254
- To delete an 254
- Reference information 255
- LED safety 256
- Warranty 256
- Reference information R-3 257
- Resetting the HP 39G/40G 258
- Reference information R-5 259
- Glossary 260
- Operating details 261
- Menu maps of the VARS menu 262
- Function aplet variables 263
- Parametric aplet variables 264
- Polar aplet variables 265
- Sequence aplet variables 266
- Solve aplet variables 267
- Statistics aplet variables 268
- Menu maps of the MATH menu 269
- R-16 Reference information 270
- Program constants 271
- Program commands 272
- Selected status messages 273
- MEMORY) 274
- Index I-1 275
- I-2 Index 276
- Index I-3 277
- I-4 Index 278
- Index I-5 279
- I-6 Index 280
- Index I-7 281
- I-8 Index 282
- Index I-9 283
- I-10 Index 284
- Index I-11 285
- I-12 Index 286
- Index I-13 287
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