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P. 333
Consider the following matrices. What is the corresponding transformation on polynomials? Indicate the domain and the
7. codomain .
(a)
(b)
(c)
(d)
(e)
Consider the space of all functions of the form where a, b, c are scalars.
8.
(a) What matrix, if any, corresponds to the change of variables , assuming that we represent a function in
this space as the vector ?
(b) What matrix corresponds to differentiation of functions on this space?
Consider the space of all functions of the form , where a, b, c, d are scalars.
9.
(a) What function in the space corresponds to the sum of (1, 2, 3, 4) and (−1, −2, 0, −1), assuming that we represent a
function in this space as the vector ?
(b) Is in this space? That is, does correspond to some choice of a, b, c, d?
(c) What matrix corresponds to differentiation of functions on this space?
Show that the Principle of Superposition is equivalent to Theorem 4.3.2.
10.
