Systems of Linear Equations [IB Math AA HL]

The speaker explains how to solve a system of three linear equations with three unknowns using row reduction to transform an augmented matrix into a form with a triangle of zeros. This allows for backward substitution to find the values of Z, Y, and X. The speaker also discusses three possible solution scenarios based on the final matrix: a unique solution (if the coefficient of Z is non-zero), no solution (if the coefficient of Z is zero but the constant term is non-zero), and an infinite number of solutions (if both the coefficient of Z and the constant term are zero).