(e) Use a nullity argument to determine whether f injective. (f) Use a rank argument to determine whether f surjective. (8) Find a matrix representation of ƒ : P₂ → R² by ƒ (az² + bx + c) = (a + coco). - (h) Find a basis for the Column Space of this matrix.

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A: Since the question has multiple subparts, as per the company guidelines, we will solve the first…

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A: From the given information we get:

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A: Since you have posted a question with multiple sub-parts we will solve first three sub-parts for…

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A: Solution is uploaded in next step

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A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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Q: Q4 let V=M₂x₂ of the form [a of with standard matrix addition and multiplication form -space-

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Q: Let T: R² → R² be defined by T = {[5].[a]} C= Given Pc 1 -2 = [223] -2 5 [T](PB (u)) = Ex: 5 ([2/2])…

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Q: im(T1 + 14T) im(14T† + T2).

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