4. Whether P3 or the space of the polynomials of degree less than or equal to...

4. Whether P3 or the space of the polynomials of degree less than or equal to 3 and consider T: P3 → P3, given by the derivation T(f) = f' . For example, T (−3x 2 + 5x - 10) = −6x + 5.

(a) Prove that T is a linear transformation.

(b) Determine ker (T).

(c) Is the T transformation injective? Justify that.

(d) The polynomial g (x) = 3x^2 + 1 belongs to the image? Justify that.

Expert Solution

milcah answered 2 years ago

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