DOWNLOAD FULL QUESTIN PAPER          👇 LIA601S Test 2 2021 Let V be the vector space of functions with basis 𝑆 = {𝑒 3𝑡 ,𝑡𝑒 3𝑡 ,𝑡 2𝑒 3𝑡 }, and let 𝑫: 𝑉 → 𝑉 be a differential operator defined by 𝑫[𝑓(𝑡)] = 𝑑𝑓(𝑡) 𝑑𝑡 ⁄ . a) Find the matrix for 𝑫 relative to the basis � b) Use the matrix obtained in part (a) to compute [3] 𝑫(2𝑒 3𝑡 − 5𝑡𝑒 3𝑡 − 4𝑡 2𝑒 3𝑡 )?     question 2 Consider the following bases of 𝑃1 𝑆1 = {6 + 3𝑥, 10 + 2𝑥} and 𝑆2 = {2, 3 + 2𝑥} a) Find the transmission matrix from 𝑆1 to 𝑆2 and denoted by 𝑃𝑆1→𝑆2 . b, b) Compute the coordinate vector [𝒑]𝑆1 , where 𝒑 = 𝑥 − 4 c, c) Hence, use the results obtained in (a) and (b) above to compute [𝒑]𝑆2 . QUESTION 3, Let 𝑇: 𝑅 3 → 𝑅 2 be a linear mapping defined by 𝑇(𝑥, 𝑦, 𝑧) = (2𝑥 + 𝑦 − 𝑧, 3𝑥 − 2𝑦 + 4𝑧). Consider the bases 𝐵1 = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and 𝐵2 = {(1, 3), (1, 4)} for 𝑅 3 and 𝑅 2 , respectively. Find the matrix representation for T relative to the bases 𝐵1 and 𝐵2,?