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the problem gives you one equation in three variables. obviously, you cannot solve for single values of x, y, and z, but you could solve for any one in terms of the other 2.
Here, they are asking for solutions in terms of the parameters s and t.
Since s and t are not in the original problem, but are "made up" by you, there is not one single correct solution.
For example, if you were to solve for z in terms of x and y, you could write x= 1(x)+ 0(y)+ 0(z), y= 0(x)+ 1(y)+ 0(z) and z= a+ b(x)+ c(y), for numbers a, b,c, so if you think of "s" and "t" as being "x" and "y" respectively, the first row of your matrix would be "0 1 0", the second row "0 0 1" and the third row "a b c".
But if you were to solve for y in terms of x and z, say as y= u+ vx+ wz, for numbers u, v, w, and then take "x" and "z" to be "s" and "t" respectively, the first row would be "0 1 0", the second row "u v w" and third row would be "0 0 1".