Solving Square Linear Systems | Linear Algebra #7
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4 سال پیش
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The seventh lecture of the "Linear Algebra" series is entitled "Introduction to Linear Equations".
Given a matrix A, there are three operations we can perform:
● Multiply a row by constant.
● Exchange two rows.
● Multiply a row by a constant and subtract it from another row.
These operations are the so-called "elementary row operations", and a matrix produced by one or more of these operations is said to be row equivalent to the original matrix. The approach we take to solving linear systems is to attach the right-hand sides as an additional column to form an n x (n + 1) matrix, i.e. the augmented matrix. Performing elementary row operations with this matrix is equivalent to performing the same operations directly on the equations. If we transform the augmented matrix to a matrix, then the two systems have the same solutions. This lecture is hence outlined as follows:
00:00 What is a Square Linear System ?
00:28 The Augmented Matrix
01:46 Elementary Row Operations
03:16 Row-equivalence of Linear Systems
04:03 Solving Square Systems through Elementary Row Operations
08:44 Summary
Lecture 1: Matrix Arithmetic Matrix Arithmetic | Linear Algebra #1
Lecture 2: Linear Transformations Linear Transformations | Linear Algeb...
Lecture 3: Powers of Matrices with Application to Graph Theory Powers of Matrices with Application t...
Lecture 4: Non-Singular Matrices and Linear Systems Non-Singular Matrices and Linear Syst...
Lecture 5: Matrix Transpose and Symmetric Matrices Matrix Transpose & Symmetric Matrices...
Lecture 6: Introduction to Linear Systems Introduction to Linear Equations | L...
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📚About
The seventh lecture of the "Linear Algebra" series is entitled "Introduction to Linear Equations".
Given a matrix A, there are three operations we can perform:
● Multiply a row by constant.
● Exchange two rows.
● Multiply a row by a constant and subtract it from another row.
These operations are the so-called "elementary row operations", and a matrix produced by one or more of these operations is said to be row equivalent to the original matrix. The approach we take to solving linear systems is to attach the right-hand sides as an additional column to form an n x (n + 1) matrix, i.e. the augmented matrix. Performing elementary row operations with this matrix is equivalent to performing the same operations directly on the equations. If we transform the augmented matrix to a matrix, then the two systems have the same solutions. This lecture is hence outlined as follows:
00:00 What is a Square Linear System ?
00:28 The Augmented Matrix
01:46 Elementary Row Operations
03:16 Row-equivalence of Linear Systems
04:03 Solving Square Systems through Elementary Row Operations
08:44 Summary
Lecture 1: Matrix Arithmetic Matrix Arithmetic | Linear Algebra #1
Lecture 2: Linear Transformations Linear Transformations | Linear Algeb...
Lecture 3: Powers of Matrices with Application to Graph Theory Powers of Matrices with Application t...
Lecture 4: Non-Singular Matrices and Linear Systems Non-Singular Matrices and Linear Syst...
Lecture 5: Matrix Transpose and Symmetric Matrices Matrix Transpose & Symmetric Matrices...
Lecture 6: Introduction to Linear Systems Introduction to Linear Equations | L...
ahmadbazzi
●▬▬▬▬▬▬▬๑۩۩๑▬▬▬▬▬▬▬▬●
_****╔═╦╗╔╦╗╔═╦═╦╦╦╦╗╔═╗**** _
_****║╚╣║║║╚╣╚╣╔╣╔╣║╚╣═╣**** _
_****╠╗║╚╝║║╠╗║╚╣║║║║║═╣**** _
_****╚═╩══╩═╩═╩═╩╝╚╩═╩═╝**** _
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4 سال پیش
در تاریخ 1398/12/09 منتشر شده
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