Let A be the matrix given below, in which a and b are real numbers. 1...

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Let A be the matrix given below, in which a and b are real numbers. 1 00 b 0 a a 0 00 a 0 0 00b A= (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A PDP-¹). - Some notes about the problem. In order to give a complete answer to part (a), you must both show that A is diagonalizable for the values you chose and show it is not diagonalizable for the other values. • Take care to organize your work clearly and explain, in detail and with words, how and why you're choosing the cases you're choosing, and how you're coming to your conclusions in each case. Your submission for this problem should be the polished final product of a larger amount of rough work. Answers which are a disorganized collage of unexplained computations will get low scores, even if those computations appear to be correct. Let A be the matrix given below, in which a and b are real numbers. 1 00 b 0 a a 0 00 a 0 0 00b A= (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A PDP-¹). - Some notes about the problem. In order to give a complete answer to part (a), you must both show that A is diagonalizable for the values you chose and show it is not diagonalizable for the other values. • Take care to organize your work clearly and explain, in detail and with words, how and why you're choosing the cases you're choosing, and how you're coming to your conclusions in each case. Your submission for this problem should be the polished final product of a larger amount of rough work. Answers which are a disorganized collage of unexplained computations will get low scores, even if those computations appear to be correct.