Linear Algebra Questions and Answers

Six people come to a party and shake hands with each other. If each person shakes the hand of every other person, how many handshakes occur?

If g(x) is primitive in R[x], prove that every nonconstant polynomial in R[x] that divides g(x) is also primitive.

Suppose A in an m x n matrix with linearly independent columns and QR factorization A = QR. Show how the formula for the least-squares solution of Ax=b (given by Theorem 6.14) can be written using the QR factorization of A. Briefly explain the advantages of the formula you give over the formula given in Theorem 6.14.