1. Let P4 be the set of all real coefficient polynomials of degree less than or equal to 4, check whether each one of the following is a basis of P4 and justify your answer using exchange theorem:
(a) {1,x,−x2,x3}.
(b) {1,1+ x,1+ x + x2,x2 + x3,x3 − x4}.
(c) {−x4,x3,−x2,x,−1}.
(d) {5,x4,x3 − x2,x2 − x,x +10,x2 −5}.
2. Textbook page 40, Chapter 3 problem 6.
3. Textbook page 40, Chapter 3 problem 7.
4. What is the dimension of C3×2 over C? Let eij a 3×2 matrix with ij-th entry equals to 1 and 0 elsewhere. Is e11,e12,e21,e22,e31,e32,e32 − e11 a basis of C3×2? Justify your answer.
