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i) prove that T is a linear transformation. ii) Find the representing matrix of t relative to the basis B=....

3. (25 points) Consider the function T: R3 -> R3 defined by T(x, y, z) = (3x, x - y, 2x + y + z).(i) Prove that T is a linear transformation. (7"'nin bir lineer donusum oldugunu gosteriniz)(ii) Find the representing matrix of T relative to the basis B = {Q1 = (1, 0,0), 02 = (1, 1,0), a3 =(1, 1, 1) } of R3.(R3 in B = {a1 = (1, 0,0), 02 = (1, 1,0), a3 = (1, 1, 1) } tabanina gore T nin matris gosterimini bulunuz.)

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