The question is;
The vectors $a_1 = (1, 1, 0)$ and $a_2 = (1, 1, 1)$ span a plane in $\Bbb R^3$. Find the projection matrix P onto the plane, and find a nonzero vector $b$ that is projected to zero.
I found the matrix $P$ as shown below, but I can't figure out how to find a nonzero vector $b$, I found only the zero vector, help me out?
Best Answer
You need a vector that is perpendicular to the plane; i.e. perpendicular to the two vectors. Their cross product is perpendicular to the vectors!