Find bases for the kernel and range of the linear transformations T in the indicated exercises. In
Question:
Find bases for the kernel and range of the linear transformations T in the indicated exercises. In each case, state the nullity and rank of T and verify the Rank Theorem.
Exercise 4
Data From Exercise 4
Let T : P2 → P2 be the linear transformation defined by T(p)x)) = xp′(x).
(a) Which, if any, of the following polynomials are in ker(T)?
(i) 2
(i) x2
(iii) 1 - x
(b) Which, if any, of the polynomials in part (a) are in range(T)?
(c) Describe ker(T) and range(T).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: