Gauss-Jordan elimination is a mathematical method used to solve systems of linear equations. It transforms a given matrix into its reduced row echelon form, making it easier to identify solutions. The process involves performing row operations, such as swapping rows, multiplying rows by non-zero constants, and adding or subtracting rows from one another. This technique is particularly useful in linear algebra for finding the values of variables in equations. By systematically simplifying the matrix, Gauss-Jordan elimination allows for straightforward interpretation of the results, revealing whether the system has a unique solution, infinitely many solutions, or no solution at all.