Interview questions 1.) Show that A is idempotent. (2) A = -5 2.) Find the inverse of A. (2) A = 13 3.) (2) Sketch the image of the line segment from (3, 1) to (-2, 4) under the translation (x, y) - (x - 2, y + 3). 4.) (2) Show that the order in which you do two dilations does not matter. 5.) (3) Solve the following: 6.) (3) Show that the composition of any two linear transformations must be a linear transformation.7.) (3) Show that a reflection can always be undone. 8.) (4) The transpose of a matrix flips the entries over the main diagonal. For example, the transpose of A is A', as shown: A = [ 21 Prove that (XY)' = Y'X' for 2 by 2 matrices. 9.) (4) Sketch the image of the shape formed by (1, 2), (4, -1) and (3, 3) under a rotation of 65 degrees, correct to two decimal places. 10.) (4) Explain why the following is not true except in special cases: (A + B) (A - B) = A2 - B2 Find a case where it is true. (A, B not equal and neither equal to I or the zero matrix and B not equal to A-3) 11.) (5) Describe the process that you would undertake to rotate any point (x,, y) around any other point (x,, v.).12.) (2, 3) a.) Prove that the area of the image of any shape in the plane transformed by the matrix T = will always be zero. b.) Show that the area of the image of the triangle formed by the points (0, 0), (2, 0) and (1, 1) under any transformation with a determinant of zero must be zero