Which of the following are subspaces of R³? Justify your answers! 

(a) The set of all vectors ( x, y, z )^T satisfying x + y + z + 1 = 0. 

(b) The set of vectors of the form ( t,−t, 0 )^T for t ∈ R. 

(c) The set of vectors of the form ( r − s, r + 2s,−s )^T for r, s ∈ R. 

(d) The set of vectors whose first component equals 0. 

(e) The set of vectors whose last component equals 1. 

(f) The set of all vectors (x, y, z)T with x ≥ y ≥ z. 

(g) The set of all solutions to the equation z = x − y. 

(h) The set of all solutions to z = xy. 

(i) The set of all solutions to x² + y² + z² = 0. 

(j) The set of all solutions to the system xy = yz = xz.