Lecturer
By the end of this lecture, students will be able to:
- Understand and apply the Gaussian Elimination method: Students will grasp the concept and process of Gaussian elimination, a systematic method for solving systems of linear equations. They will learn to manipulate equations into a form that simplifies solving for multiple variables in a step-by-step manner.
- Perform matrix row operations to transform a system of equations into an upper triangular form: Students will develop the ability to convert systems of equations into matrix form and apply row operations, such as row swapping, scaling, and row addition/subtraction. These skills will be used to achieve an upper triangular matrix, where zeros are created below the diagonal, making the system easier to solve.
- Utilize back substitution to find the solution for each variable: After transforming the system into an upper triangular matrix, students will practice using back substitution. This involves solving the last equation first (which has only one unknown) and then substituting that value into previous equations to find the values of other unknowns.
- Understand and apply the Gauss-Jacobi method: Students will explore the Gauss-Jacobi iterative method, which approximates solutions for systems of linear equations by using successive approximations. They will learn how to iteratively update each variable using the values from the previous iteration and apply this method in scenarios where iterative refinement is advantageous, particularly for larger systems.
Material File