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(a)Write down a 3x3 matrix M whose entries are all zeros or ones. Your matrix should contain at least three ones and should not be all ones. (i) Draw the digraph which is represented by the adjacency matrix M. (ii) Calculate the reachability matrix M*, explaining all the steps in yoursolution. (iii) Interpret your reachability matrix M* in terms of the digraph you drew in(a)(i). I.e., what does the reachability matrix M* tell you about your digraph? (b) Write down a 2x2 matrix S whose entries are non-zero integers between -5 and 5. (i) A square has vertices A(1,-1), B(1,1), C(-1,1) and D(-1,-1). Find the images A', B', C' and D' of each of these vertices under the transformation S. (ii) Plot the transformed square and describe the geometric transformation which has taken place. (c) (i) Write down a 2x2 matrix T whose entries are non-zero integers between -5 and 5, and whose determinant is not zero. (ii) Find the products ST and TS where S is your matrix from (b). (iii)Find the inverse of your matrix T. (iv) Write down the system of equations represented by the matrix equation T(x) = (-¹). Use your answer to (iii) to find the solution to the system.

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