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Let $A = {X = (x, y, z)^T : PX = 0 \text{ and } x^2 + y^2 + z^2 = 1}$, where $P = \begin{bmatrix} 1 & 2 & 1 \ -2 & 3 & -4 \ 1 & 9 & -1 \end{bmatrix}$, then the set $A$:
(1) is a singleton
(2) is an empty set
(3) contains more than two elements
(4) contains exactly two elements
BETA
