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Solving Linear Systems of Equations Using Augmented Matrix and Row Operations
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Are you looking for a powerful method to solve linear systems of equations? In this video, we introduce you to the augmented matrix and row operations, which provide an efficient and straightforward approach to solving linear systems.
We start by introducing the concept of an augmented matrix, which is simply a matrix that contains both the coefficients of the variables and the constants of the equations. We then show how to use row operations such as swapping, scaling, and adding to manipulate the matrix and transform it into row echelon form, and then further into reduced row echelon form.
We explain how the solutions of the linear system can be easily read off from the reduced row echelon form, and how to handle cases where the system has no solution or infinitely many solutions. We also demonstrate the advantages of using this method over other methods, such as the substitution or elimination method.
Throughout the video, we provide numerous examples and step-by-step explanations to help you understand the process of solving linear systems using the augmented matrix and row operations. Whether you are a student of mathematics or a practitioner in a field that requires linear algebra, this video will provide you with a solid foundation in solving linear systems using this powerful method.
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We start by introducing the concept of an augmented matrix, which is simply a matrix that contains both the coefficients of the variables and the constants of the equations. We then show how to use row operations such as swapping, scaling, and adding to manipulate the matrix and transform it into row echelon form, and then further into reduced row echelon form.
We explain how the solutions of the linear system can be easily read off from the reduced row echelon form, and how to handle cases where the system has no solution or infinitely many solutions. We also demonstrate the advantages of using this method over other methods, such as the substitution or elimination method.
Throughout the video, we provide numerous examples and step-by-step explanations to help you understand the process of solving linear systems using the augmented matrix and row operations. Whether you are a student of mathematics or a practitioner in a field that requires linear algebra, this video will provide you with a solid foundation in solving linear systems using this powerful method.
THE BEST THING TO DO ON THIS CHANNEL IS TO LIKE, SUBSCRIBE/COMMENT AND SHARE THE VIDEOS . THIS IS REALLY APPRECIATED
Use Translation Property to compute L(e^atcosbt)|Engineering Math
UPDATED: "Unlocking the Inverse Laplace Transform: A Beginner's Journey "|Table 7.4|
Unveiling the Secrets of Eigenvalues and Eigenvectors for 2x2 Matrices (I)
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
How to Find Eigenvalues and Eigenvectors of 3x3 Matrices (I)
Unveiling the Secrets of Eigenvalues and Eigenvectors for 2x2 Matrices (I)
Determine the Laplace Transform of the given function using Table 7.1 and the properties in Table7.2 : Determine the Laplace Transform of the given function using Table 7.1 and the properties in Table7.2
"Solve Bernoulli Differential Equation with Ease: A Step-by-Step Guide" |Part V
Step-by-Step Guide to Solving Separable Differential Equations | Lesson A (UPDATED)
"How to use Reduction of Order to solve Second Order Differential Equations"| Lesson 73
"The Relationship between the Roots and Coefficients of Quadratic Equations" | Lesson 5
Solving Trigonometric Equations with Multiple Angles (III) | Lesson 26
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"Partial Fraction Decomposition: Simplifying Complex Fractions " |Part 3
Trigonometric Ratios for Acute Angles: Definitions and Examples | Lesson 5
Trigonometry Addition Formulae (III) :Questions and Solutions | Lesson 11
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