Description
1. Let P
4 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 P
4
and justify your
answer using exchange theorem:
(a) {1, x, −x
2
, x3}.
(b) {1, 1 + x, 1 + x + x
2
, x2 + x
3
, x3 − x
4}.
(c) {−x
4
, x3
, −x
2
, x, −1}.
(d) {5, x4
, x3 − x
2
, 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 C
3×2 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
C
3×2
? Justify your answer.
