first row reduce and switch the rows a bit to yield S= [1,0,0,0],[0,a,0,0],[0,0,1,0],[0,1,0,a-1]. I presume you already know that if the rows of S are linearly dependent, then that must mean one of the rows is a linear combination (or scalar multiple) of the others. It becomes apparent that S is linearly dependent when a=0 or a=1. When a=0 the 2nd row is all zeroes, and a row of all zeroes is just a linear combination of the other rows multiplied by zero. When a=1 the 4th and 2nd row are scalar multiples of each other. (4th row times a = 2nd row)