The word matrix has become mainstream in 1999 thanks to the movie The Matrix. Long before that, the word had been in use in science and technology. In mathematics and physics (the fields I am most often confronted with in talks and discussions), a matrix is a regular array of objects such as numbers or functions. There are two different pronunciations typically used by non-native speakers. First, there is [ˈmeɪtrɪks], with the letter a pronounced as in late or hate. This pronunciation is listed as the correct one in the Oxford Advanced Learner’s Dictionary (listen to the word here), and also in Longman’s Pronunciation Dictionary. The alternative pronunciation used by non-native speakers is [ˈmætrɪks], listen here,
with the letter a pronounced as in cat or hat. This second version, while not mentioned in the Oxford Dictionary, is according to the Longman Dictionary only used in the field of printing. As far as I remember, the movie exclusively used the first variant, [ˈmeɪtrɪks], and I do not recall hearing a native English speaker say [ˈmætrɪks] in a scientific talk.
PS: German speakers may be interested to know that the words Matrize and Matrix are not interchangeable, see here.