Let P₂ be the vector space of polynomials of degree at most Let T: P₂ → P₂ by T (p(x)) = p(x) + x p(x). a) Show that T is a linear transformation b) Determine the kernal of T c) Show that T is an isomorphism d) Determine T-¹

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A: Here we can use the composition of function formula to find the required values.

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A: Note:  As you requested only Part C(I) so I answered here only that.

Q: Let T: V-->W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

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A: The kernel is a line with slope -1 and passes through the origin.

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A: we have to  prove that T is a linear transformation .Then have to determine whether T is a

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A: I am solving the first part for you.The given linear transformation is : from To find all vectors…

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A: Follow the steps.

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