(b) It is a fact that the linear relations of the columns of a matrix are not changed by row [6] reduction. Let b1, b2, b3, b4, b5, b6 be the columns of B, and let a1, a2, a3, a4, a5, a6 be the columns of A. By observing the columns of B we can easily see that which tells us that which would have been di?cult to determine without B. Express b5 and b6 as linear combinations of b1, b2 and b4. Check that these combinations also produce combinations for a5 and a6 as linear combinations of a1, a2 and a4