Question: (i) Consider the vector space R2. Find the transition matrices P and P' with respect to the bases B = {(1,2), (3,0)] and B' =

(i) Consider the vector space R2. Find the transition matrices P and P' with respect to the bases B = {(1,2), (3,0)] and B' = {(2,1), (3,2)]. (ii) Sketch the image of the square with vertices at (0.0). (2.0). (2.2). (0. 2) with transformation T: R2 - R2 defined by T(x) = Ax where matrix A = (iii) Sketch the image of the triangle with vertices (1, 3). (3, 3) and (2, 8) with transformation T: R2 - R2 defined by T(x) = (x7) + (2) (6+2+2) 11) Find an orthonormal basis wtih basis B = {(1,0,0,0), (0, -1,1,0), (0, -1,1,1), (0,0,1,0)} for R4. 12)

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