Question: Let A and B be invertible 2 2 matrices with complex entries. (a) Prove that there always exists a scalar z C such that the

Let A and B be invertible 2 2 matrices with complex entries.

(a) Prove that there always exists a scalar z C such that the matrix 21A zB is not invertible. Solution: (2pt)

(b) Provide an example of invertible matrices A and B such that

the matrix 21A zB is invertible for all z C except for z = 21. Justify your answer. Solution:

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