a) Determine a condition under which (x, y, z) is a linear combination of [-3, 5, -3], [-9, 11, -3], [-6, 8, -3]? Your condition should take the form of a linear equation.
Im so confused?? I have the theorem that every vector (x, y, z) in R^3 is a linear combination of x(1, 0, 0) + y(0, 1, 0) + z(0, 0, 1).
HINT
In general we need to write down the system
$$av_1+bv_2+cv_3=(x,y,z)$$
in augmented matrix form and handle it by RREF to find the condition on x,y,z for the system to have solution.
Note that this approach gives the cartesian equations of the subspace spanned by $v_1,v_2,v_3$.
As an alternative look for the dimensions of the subspace, if you find dim=3 then the linear combination always has solution. Otherwise select a basis and solve the system for the basis vectors.