If two m n matrices A and B are close in the sense that A B 2 for some small positive number6, then their pseudoinverses will also be close that is, A B 2 , for some small positive number In the case of a true statement, explain or prove your answer In the case of a false statement, give an example to show that the statement is not always true

Question: If two m n matrices A and B are close in the sense that ||A - B||2 < for some small positive number6,

If two m × n matrices A and B are close in the sense that ||A - B||2 < ∈ for some small positive number6, then their pseudoinverses will also be close; that is, ||A+ - B+||2 < δ, for some small positive number δ.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.

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