The number of arrangements that can be made by using all the letters of the word ‘MATRIX’ so that the vowels may be in the even places is 

The given word is $MATRIX$

The vowels are $A,I$

Since there are six places, the even places are $2,4,6$

These three places can be filled by two ovels in $3_{P_2}=6$ ways

The remaining four places with remaining four letters can be filled in $4!$ ways

Therefore, the required number of arrangments is $6·4!=\boxed{144}$