How to return TRUE if matrix contains any NAs?

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I wish query a matrix object and return a simple TRUE/FALSE answer if a matrix contains any NAs. So, if there are no NAs present you would get FALSE.

is.na(my.matrix) will tell me element-by-element if NAs are present, but I don't know how to sum up the results into a single answer. na.fail() looks like a better bet, but I'm still not sure how to extract a straightforward TRUE/FALSE answer.

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