(a) Let B = {e¹, tet, t²e¹} and let V = spanB. Let D: V → V be the linear operator given by D(ƒ) = f'. (i) Find the B-ma

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A Let B E Tet T E And Let V Spanb Let D V V Be The Linear Operator Given By D F F I Find The B Ma 1 (88.22 KiB) Viewed 7 times

(a) Let B = {e¹, tet, t²e¹} and let V = spanB. Let D: V → V be the linear operator given by D(ƒ) = f'. (i) Find the B-matrix of D. (ii) Find all eigenvalues of D. (iii) For each eigenvalue you found in part (ii), find a basis the corresponding eigenspace. = (b) Let B = {1, x, x²} and let V P₂ (R). Let TV → V be the linear operator given by T(p(x)) = p(0) + 3p(1)x + p(2)x². (i) Find the B-matrix of T. (ii) Find all eigenvalues of T. (iii) For each eigenvalue you found in part (ii), find a basis the corresponding eigenspace.