Mrs Brown has pet cats, pet parrots, pet fish and pet rocks. Each pet rock has three eyes, no legs and no tail. The other pets have as many of these features as you would expect. Let the number of cats, parrots, fish and rocks be given by c, p, f and r respectively.
(a) Suppose N = [ c p f r ]^T. Find the matrix M so that MN is the matrix whose entries are: the total number of eyes, legs and tails of Mrs Brown’s pets.
(b) Together, Mrs Brown’s pets have 25 eyes, 14 legs and 8 tails. How many pets of each type might she have? Explain your answer carefully.
I'm not sure if part b needs me to state just the general expressions or find actual solutions because it seems to me that the system has infinitely many solutions, i.e. total number of eyes ( 2c + 2p + 2f + 3r = 25 ), legs ( 4c + 2p = 14 ) and tails ( c + p + f = 8 ).