Question: Consider the following 2 x 2 matrix: H3 3] When is this matrix diagonalizable? (In other words: under what conditions on a and b can

Consider the following 2 x 2 matrix: H3 3] When is this matrix diagonalizable? (In other words: under what conditions on a and b can this matrix be diagonalized?) Consider the following 2 x 2 matrix: Diagonalize this matrix for n 2 2. Note: There exists a simple formula for the inverse of a 2 X 2 matrix which may help with this problem: a b '1_ 1 d c d _adibc c a (c) Again, consider the matrix: An = n 1 n Let f(.) be any analytic function. (As discussed in lecture: for this class, we can simply treat analytic functions as infinitely differentiable functions.) Calculate f(An), and take the limit as n -+ 0o

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