[SOLVED] Math 231 — hw 13

1. Suppose p0, p1, p2, p3 is a basis of the space of polynomials of degree 3. Construct a
basis where none of the polynomials are degree 2.
Recall: the degree of a polynomial is the term with the maximum degree, for example
this polynomial is degree 3: x
3 + x
2 + x + 1.
2. Suppose {v1.v2, v3, v4} is basis of V . Prove that
{v1 + v2, v2 + v3, v3 + v4, v4}
is also a basis of V .
3. Suppose v1.v2, v3, v4 is basis of V . Prove that
{v1, v1 + v2, v1 + v2 + v3, v1 + v2 + v3 + v4}
is also a basis of V .