The image of a 3 4 matrix is a subspace of R4.

Math241Lecture 2: Equation of planes, Quadratic Surfaces Recall from the previous lecture that we can find an equation of a line just by knowing a point on the line and a vector parallel to the line. We can do a similar thing with the equation of a plane. Say we know a point P on the plane with coordinates P=(x ,y,z) . Next, say we want a vector perpendicular to the point. We call that a normal vector and denote it as ⃗=¿a,b,c>¿ . We do not need that the normal vector is on the plane. It just has to be P perpendicular to it. Now let’s take a random point on the plane and call it with coordinates P1=(x 1 y 1z 1 r r1 P