Description
1. In class, we discussed the differential operator, D, over the space P3, the space of polynomials up to degree 3. The differential operator takes polynomials to their derivatives.
Solve the following equation: D(ax3 + bx2 + cx + d) =
2. If ax3 + bx2 + cx + d is represented as the column vector
a
b
c
d
,
write out M(D). (Hint: Use your previous answer.)
3. In class, we stated that the null D is the space of constant functions. What is the
representation of this null space? In other words, what is null M(D)?
4. Suppose S is a map that represents a shift in vectors over R
3
. S(a, b, c) = (b, c, 0).
Describe its null space and give a representation M(S).
5. Now suppose we define a function P that represents a permutation over the vector
space R
3
. P(a, b, c) = (b, c, a). Describe its null space and give a representation M(P).