Can I nest an array in a table?

In my code I have this:

\begin{equation*}
\left.
\begin{array}{rcl}
    2x\lambda &=& 2 \\
    2y\lambda &=& 3 \\
    2z\lambda &=& 4 \\
    x^2+y^2+z^2 &=& 1 \\
\end{array}
\right\}
enter code here`\end{equation*}

$(x,y,z)\neq (0,0,0)$:

\begin{align*}
\frac{1}{x} = &\lambda = \frac{3}{2y} \\
\frac{1}{x} = &\lambda = \frac{2}{z} \\
\end{align*}

\begin{align*}
    y &= \frac{3}{2}x \\
    z &= 2x
\end{align*}

Which is using a lot of space in my document. So I'm wondering if I can do something like this:

I tried several ways but I only can do it without the brace. But the brace is necessary. Can somebody help me?