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Question 1 – 15 marks

You should be able to answer this question after studying Unit 6.

(a) For each of the following linear transformations, write down its matrix and describe its type. (i) g(x,y) = (2x,7y) (ii) h(x,y) = (x,3x + y) (iii) k(x,y) = (y,x) [5]

(b) Use the matrices that you found in part (a) to show that the linear transformation f = k◦h◦g is represented by the matrix A =6 7 2 0. [2] (c) Show that f is invertible, and find the matrix that represents f−1. [2] (d) Find the equation of the image f(C) of the unit circle C, in the form ax2 + bxy + cy2 = d,

where a, b, c and d are integers whose values you should find. [5] (e) Calculate the area enclosed by f(C). Get mathematics  assignment homework help today