It looks like your Matthew Walker, was born 27/Dec/1835. New Cumnock, Ayr. to parents Hugh Walker, and Jean Lammie.
This birth is from Scotlandspeople. and his full name is Matthew Kirkland Walker.
In 1861. census Dalry, Ayr. he is living with Wife Lillias, and son Hugh. aged 2 months.
Next door, or its maybe the same house, are his parents and siblings.