Plz do only Part C (I) Only please (a) A linear operator T on R³ maps v₁ = (1, −3,−4) to v₂ = (2, 7, −8) andV3 = (-2, 5, 0) to V₁ = (-1,1,-12).i. Does the above information uniquely determine T(v₂)? If so, find it.ii. Does the above information uniquely determine T(v₁)? If so, find it.Justify your reasoning.(b) Consider the following set S of points in the plane: {(1, −2), (2, 1), (4, 1)}.Find a value of a such that S and the set S' obtained by adding the point(0, a) to S have the same least squares straight line fit. Show your working.=(c) For a polynomial p ao + a₁x + a₂x² + ... + anxn, let p denote thepolynomial obtained from p by removing the constant term, i.e. p = p-ao.Consider the vector space P of all polynomials and let T: P→ Po bethe linear map defined as follows:T(p) = p + xp',where p' is the derivative of p.=For example, if p 2 + 5x x² then pT(p) = 5x x² + x(5 - 2x) = 10x - 3x².--=5x - x², p' = 5 - 2x andi. Find a basis for the kernel of T.ii. What is the range of T?iii. Compute the eigenvalues of T and an eigenvector corresponding to

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(c) For a polynomial p = a + a₁x + a₂x² + + anx", let p denote the polynomial obtained from p by removing the constant term, i.e. p = p-ao. Consider the vector space P of all polynomials and let T: P→ Po be the linear map defined as follows: T(p) = p + xp', where p' is the derivative of p. For example, if p = 2 + 5x − x² then p = 5x - x², p' = 5 - 2x and T(p) = 5x - x² + x(5-2x) = 10x - 3x². i. Find a basis for the kernel of T. ii. What is the range of T? iii. Compute the eigenvalues of T and an eigenvector corresponding to