HP 49g+ Graphing Calculator Manual de usuario Pagina 124
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Page 9-8
This system of linear equations can be written as a matrix equation, A
n
×
m
⋅x
m
×
1
= b
n
×
1
, if we define the following matrix and vectors:
mn
nmnn
m
m
aaa
aaa
aaa
A
×
=
L
MOMM
L
L
21
22221
11211
,
1
2
1
×
=
m
m
x
x
x
x
M
,
1
2
1
×
=
n
n
b
b
b
b
M
Using the numerical solver for linear systems
There are many ways to solve a system of linear equations with the calculator.
One possibility is through the numerical solver ‚Ï. From the numerical
solver screen, shown below (left), select the option 4. Solve lin sys.., and
press @@@OK@@@. The following input form will be provide (right):
To solve the linear system A⋅x = b, enter the matrix A, in the format [[ a
11
,
a
12,
… ], … [….]] in the A: field. Also, enter the vector b in the B: field.
When the X: field is highlighted, press @SOLVE. If a solution is available, the
solution vector x will be shown in the X: field. The solution is also copied to
stack level 1. Some examples follow.
The system of linear equations
2x
1
+ 3x
2
–5x
3
= 13,
x
1
– 3x
2
+ 8x
3
= -13,
2x
1
– 2x
2
+ 4x
3
= -6,
can be written as the matrix equation A⋅x = b, if
- Printing History 2
- Preface 3
- Table of Contents 4
- Page TOC-2 5
- Page TOC-3 6
- Page TOC-4 7
- Chapter 8 – Vectors 8
- Page TOC-6 9
- Page TOC-7 10
- Limited Warranty – W-1 11
- Chapter 1 12
- Getting started 12
- The TOOL menu 14
- Setting time and date 15
- Page 1-5 16
- Selecting calculator modes 17
- Operating Mode 18
- Page 1-8 19
- Page 1-9 20
- Page 1-10 21
- Page 1-11 22
- Page 1-12 23
- Page 1-13 24
- Angle Measure 25
- Coordinate System 26
- Selecting CAS settings 27
- Selecting Display modes 28
- Selecting the display font 29
- Page 1-19 30
- Page 1-20 31
- Chapter 2 33
- Introducing the calculator 33
- Page 2-2 34
- Page 2-3 35
- Page 2-4 36
- Page 2-5 37
- Page 2-6 38
- Page 2-7 39
- Page 2-8 40
- The HOME directory 41
- Subdirectories 41
- Variables 42
- Creating variables 43
- Page 2-12 44
- Page 2-13 45
- Checking variables contents 46
- Page 2-15 47
- Deleting variables 48
- UNDO and CMD functions 49
- CHOOSE boxes vs. Soft MENU 49
- Page 2-18 50
- Page 2-19 51
- Chapter 3 53
- Page 3-2 54
- Page 3-3 55
- Page 3-4 56
- Page 3-5 57
- Page 3-6 58
- Page 3-7 59
- Operations with units 60
- Page 3-9 61
- Available units 62
- Attaching units to numbers 63
- Page 3-13 65
- Unit conversions 66
- Page 3-15 67
- Defining and using functions 68
- Page 3-17 69
- Chapter 4 71
- Entering complex numbers 72
- Page 4-3 73
- The CMPLX menus 74
- CMPLX menu in keyboard 75
- Page 4-6 76
- Chapter 5 78
- Page 5-2 79
- Page 5-3 80
- Functions in the ALG menu 81
- Page 5-5 82
- Page 5-6 83
- Page 5-7 84
- Polynomials 85
- Page 5-9 86
- Fractions 87
- The PROPFRAC function 88
- The PARTFRAC function 88
- The FCOEF function 88
- The FROOTS function 89
- Chapter 6 91
- Solution to equations 91
- Function SOLVE 92
- Page 6-3 93
- Function SOLVEVX 94
- Function ZEROS 94
- Numerical solver menu 95
- Polynomial Equations 96
- Page 6-7 97
- Page 6-8 98
- Financial calculations 99
- Page 6-10 100
- Page 6-11 101
- Reference 102
- Chapter 7 103
- Operations with lists 103
- Page 7-2 104
- Functions applied to lists 105
- Lists of algebraic objects 106
- The MTH/LIST menu 106
- Lists of complex numbers 106
- Page 7-5 107
- The SEQ function 108
- The MAP function 108
- Chapter 8 109
- Page 8-2 110
- Page 8-4 112
- → keys are selected 112
- Changing sign 113
- Absolute value function 114
- The MTH/VECTOR menu 115
- Chapter 9 117
- Page 9-2 118
- Operations with matrices 119
- Multiplication 120
- .,,2,1;,,2,1 121
- Page 9-6 122
- Solution of linear systems 123
- Page 9-8 124
- Page 9-9 125
- References 126
- Chapter 10 127
- Graphics 127
- Page 10-2 128
- Page 10-3 129
- Page 10-4 130
- FUNCTION, press the 130
- Fast 3D plots 131
- Page 10-6 132
- Page 10-7 133
- Chapter 11 135
- Calculus Applications 135
- )(lim xf 136
- CxFdxxf += 137
- Infinite series 138
- Page 11-5 139
- Chapter 12 141
- Multiple integrals 142
- [] [] [] [] 143
- FdivF •∇= 144
- FF ×∇=curl 144
- Chapter 14 145
- Differential Equations 145
- Function LDEC 146
- .)3/exp()3/exp(5)( 147
- Cdxxxxy +⋅⋅−⋅= 147
- The variable ODETYPE 148
- Laplace Transforms 149
- Fourier series 150
- Page 14-7 151
- Chapter 15 153
- Probability Distributions 153
- Random numbers 154
- The MTH/PROB menu - part 2 155
- Chapter 16 157
- Statistical Applications 157
- Type: Population in the 158
- Page 16-4 160
- Page 16-5 161
- Confidence intervals 163
- Page 16-8 164
- Hypothesis testing 165
- Page 16-10 166
- Chapter 17 168
- Numbers in Different Bases 168
- Chapter 18 170
- Page 18-2 171
- Limited Warranty 172
- Service 173
- Page W-3 174
- Regulatory information 175
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