Question: Give an example of a linear transformation whose kernel is the plane x + 2y + 3z = 0 in |R3.

I'm lost here. I found the vectors [1, 1, -1] and [-5, 4, -1] span the Kernel, but I really have no idea where to go from here... would it be the product of the matrices that have kernels in the two lines in the direction of the two vectors?