find a matrix that has s10cd1 as its only special solution t

find a matrix that has s_1=(0,c,d,1) as its only special solution to Ax=0 or explain why its impossible to do so.

Solution

Here given system is homogeneous system of equations. Hence solution alway exists. That maybe unique or many solution s.

If we observed the solution that contains one variable as 1 , this is impossible . because two variables are parameters , remaining two are either parameter or zeros. . So this solution is impossible