Question: 1. Consider the 6 x 6 matrix A = [1 0 0 1 1 1 0 1 0 1 1 1 0011 11 000100

1. Consider the 6 x 6 matrix A = [1 0 0

1. Consider the 6 x 6 matrix A = [1 0 0 1 1 1 0 1 0 1 1 1 0011 11 000100 000010 00000 1 (a) [2 marks] Compute A. [Hint: Partition A as a block matrix to save yourself a lot of work.] (b) [1 mark] What do you think 42023 equals? You do not have to rigorously prove your answer is correct, but briefly explain why you think it's true. B-1] 2. [2 marks] Suppose z is a real number, A== for which AB and B Find all values of 3. Let T: R R2 be the linear transformation with the property that T(1,-1)= (-1,-1) and T(0, 1) = (2,4). (a) [2 marks] Illustrate the geometric effect of T. In particular, show where T sends (1,-1) and (0, 1), and thus how it distorts a parallelogram grid with those two vectors as sides. (b) [2 marks] Find [7], the standard matrix of T.

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