Determinants for Solving System of Linear Equations: Cramer’s Rule

Here is a simple description you can use for your YouTube video: In this lesson, we learned how to solve a system of three linear equations using Cramer’s Rule and determinants. We started with the system of equations: x + 2y - 3z = 5 x - y + 2z = -3 x + y - z = 2 First, we wrote the coefficients of the variables as a 3 × 3 coefficient matrix A. Then, using determinants, we calculated the determinant of matrix A. After that, we replaced each column of A with the constants column to create three new matrices: Nx, Ny,and Nz. By finding the determinants of these matrices, we were able to apply Cramer’s Rule. Finally, after calculating the four determinants, we found the solution of the system: x=0, y=1,z=-1 This lesson shows how determinants provide a powerful method for solving systems of equations and how matrix operations can simplify complex algebraic problems. Cramer’s Rule is an important connection between algebra and linear algebra, helping students understand how equations, matrices, and determinants work together.