jee-advanced 2009 Q32

jee-advanced · India · paper2 Matrices Linear System and Inverse Existence
Let $(x,y,z)$ be points with integer coordinates satisfying the system of homogeneous equations: $$\begin{array}{r} 3x-y-z=0\\ -3x+z=0\\ -3x+2y+z=0 \end{array}$$ Then the number of such points for which $x^{2}+y^{2}+z^{2}\leq100$ is
Let $(x,y,z)$ be points with integer coordinates satisfying the system of homogeneous equations:
$$\begin{array}{r}
3x-y-z=0\\
-3x+z=0\\
-3x+2y+z=0
\end{array}$$
Then the number of such points for which $x^{2}+y^{2}+z^{2}\leq100$ is