Determine for all values of the parameter p whether the statement $d\in <a,b,c>$ holds for the vectors $a,b,c,d\in {R}^{4}:$ $a=3,-1,2,1{)}^{T}$ , $b=(15,8,8,7{)}^{T}$ , $c=(12,6,7,p{)}^{T}$ , $d=(6,8,-9,12{)}^{T}$

d is a subspace of a,b,c ? How can we find all values of the parameter p?

d is a subspace of a,b,c ? How can we find all values of the parameter p?