Hi everyone, I am working on the following problem. Suppose the set of vectors X1,..,Xk is a basis for linear space V1. Suppose the set of vectors Y1,..,Yk is also a basis for linear space V1. Clearly the linear space spanned by the Xs equals the linear space spanned by the Ys. Construct an algebraic argument to show that X(X'X)^(-1)X'=Y(Y'Y)^(-1)Y' I am very confused, I am not sure what is meant by algebraic argument in this instance, and I would welcome your ideas on how to tackle this question. Thanks in advance.