a Find a basis for the set of vectors in R3 in the plane x

a. Find a basis for the set of vectors in R3 in the plane x + 2y - 3z = 0

Any two non-colinear vector can span the space that is spanned by the plane (x + 2y - 3z) = 0

(1 2 -3)(x y z)^T = 0, where T represents the transpose of the matrix

So the basis vector can be x=3,y=0,z=1

x = 2, y=-1 and z=0

Hence the two basis vectors that can span this plane in R3 is given by

[ 3 0 1]^T and [2 -1 0]^T

where T represents the transpose of the matrix