QR factorization decomposes a matrix A into an orthogonal matrix Q and an upper triangular matrix R (A=QR). Householder reflections create Q, but for overdetermined systems (many rows, few columns), Q becomes very large. Reduced QR factorization solves this by storing only the relevant parts of Q and R, improving efficiency for least squares problems. This segment explains the challenges of using the Householder method for solving overdetermined systems of equations where the number of rows (samples) significantly exceeds the number of columns (variables). It highlights how the resulting Q matrix becomes excessively large, impacting computational efficiency, and emphasizes the need for alternative approaches to address this issue, particularly in least squares problems where only a few variables need to be solved.