Question 4.1.4: Define a mapping T: P3 → P2 by T (p(x)) = p′(x)where p′(x) i...
Define a mapping T : P_{3} → P_{2} by
T (p(x)) = p^{\prime } (x)
where p^{\prime } (x) is the derivative of p(x).
a. Show that T is a linear transformation.
b. Find the image of the polynomial p(x) = 3x³ + 2x² − x + 2.
c. Describe the polynomials in P_{3} that are mapped to the zero vector of P_{2} .
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