From the course: Machine Learning Foundations: Linear Algebra
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Solving linear equations using Gaussian elimination
From the course: Machine Learning Foundations: Linear Algebra
Solving linear equations using Gaussian elimination
- [Instructor] Solving linear equations manually becomes tedious each time there are three or more equations. In the 1800s, a brilliant German mathematician called Karl Gauss invented the method that is used for solving a system of linear equations, and in his honor, that method is called Gaussian elimination. It involves concatenating the matrix A and vector B into a form called an augmented matrix, and then performing a series of elementary row operations on the augmented matrix in a particular order. At the end, we will have three possible situations. Get the solution of the system, the system won't have a solution, or the system will have an infinite number of solutions. To create an augmented matrix, we will take the regional matrix A and combine it with the constant vector B. Let's see it in the following example. The vertical line between the matrix indicates the separation between A and B. Now, we will directly…
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