(Strang 4 Ed Intro to LA, #2.2.18)
The plane x-3y-z = 12 is parallel to the plane x-3x-z=0, (which has special sols (3,1,0) and (1,0,1) ). One point on the plane is 912,0,0). All points on the plane have the form (fill in the first components A, B, C)

x A B C
y = 0 +y 1 +z 0
z 0 0 1

I think it's A=12, B=3 and C=1, the particular solution + the null space for the parallel plane. Is that correct? (the answer key says B=4, not 3).

Question

(Strang 4 Ed Intro to LA, #2.2.18)
The plane x-3y-z = 12 is parallel to the plane x-3x-z=0, (which has special sols (3,1,0) and (1,0,1) ). One point on the plane is 912,0,0). All points on the plane have the form (fill in the first components A, B, C)

x       A        B         C
y  =   0   +y 1   +z 0
z       0        0         1

I think it's A=12, B=3 and C=1, the particular solution + the null space for the parallel plane. Is that correct? (the answer key says B=4, not 3).