Linear Systems and Equations
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System of Linear Equations
m
equations
n variables
In this course, m and n can be large
多元一次聯立方程式
coefficient
Linear System
= System of Linear Equations
Linear
System
Trivial!
Next page
Linear
System
Linear
System
Linear
System
……
Linear
System
standard (unit) vector
(only one element is “1”,
the rest elements are “0”)
Linear
System
Linear
System
Linear
System
……
Linear
System
standard (unit) vector
(only one element is “1”,
the rest elements are “0”)
Linear
System
Linear
System
Linear
System
……
……
Linear
System
……
……
……
Linear systems and systems of linear equations are essential concepts in mathematics. These systems consist of equations with coefficients and variables, and solving them involves finding values that satisfy all equations simultaneously. The images provided illustrate the structure of linear systems and equations, showcasing examples with different coefficients and variables. Standard unit vectors play a key role in representing solutions to these systems. By following through the visual representations, one can deepen their comprehension of linear systems and enhance problem-solving skills in mathematics.
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Presentation Transcript
Linear System = Linear System = System of Linear Equations System of Linear Equations
System of Linear Equations coefficient m equations n variables In this course, m and n can be large
Linear System = System of Linear Equations ?1 ?2 ?1 ?2 Linear System ?? ?? Next page Trivial!
A linear system A system of linear equations ?11 ?21 ?12 ?22 ?1? ?2? 1 0 0 1 0 0 Linear System Linear System Linear System ??1 ??2 ??? 0 0 1 standard (unit) vector (only one element is 1 , the rest elements are 0 ) ?1 ?2 Linear System ??
A linear system A system of linear equations ?11 ?21 ?12 ?22 ?1? ?2? 1 0 0 1 0 0 Linear System Linear System Linear System ??1 ??2 ??? 0 ?? 0 ?? 1 ?? ?1 ?2 1 0+ ?2 0 1 standard (unit) vector (only one element is 1 , the rest elements are 0 ) ? = = ?1 = ?1??+ ?2?? ?1 ?2 Linear System ??
A linear system A system of linear equations ?1 ?1 ?2 ?? ?2 ?? ?11 ?21 ?12 ?22 ?1? ?2? 1 0 0 1 0 0 Linear System Linear System Linear System ??1 ??2 ??? 0 0 1 ?1 0 ?2 0 0 0 0 ?? 0 ?1 ?2 Linear System ??
