(a) If Matrix A and B are orthogonal, determine whether the following are orthogonal or not Give full justifications for your answer (i) A T, (ii) B , (iii) B AB (b) Consider the transformation f R R given byf(x,y) (x 2y,x y, 2x 3y) Show that f is a linear transformation Find a matrix form of this transformation

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Question: (a) If Matrix A and B are orthogonal, determine whether the following are orthogonal or not. Give full justifications for your answer.(i) A^T, (ii) B-,

(a) If Matrix A and B are orthogonal, determine whether the

(a) If Matrix A and B are orthogonal, determine whether the following are orthogonal or not. Give full justifications for your answer.(i) A^T, (ii) B-¹, (iii) B-¹ AB.(b) Consider the transformation f: R² R³ given byf(x,y) = (x+2y,x-y,-2x+3y).Show that f is a linear transformation. Find a matrix form of this transformation.

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