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I need to find the null space of:

[tex]\dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right)[/tex]

so:

[tex]\dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right) \binom{x}{y} = 0[/tex]

I'm not sure how to go about doing this because I've been staring at:

[tex](cos(\beta)-1)x=-sin(\beta)e^{-i \alpha} y[/tex]

[tex]sin(\beta) e^{i \alpha} x = (-cos(\beta)-1) y[/tex]

for a while now and I'm not sure how to get the x and y values

[tex]\dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right)[/tex]

so:

[tex]\dotx \left(\begin{array}{cc}cos(\beta)-1&sin(\beta)e^{-i \alpha}\\sin(x)e^{i \alpha}&-cos(\beta)-1\end{array}\right) \binom{x}{y} = 0[/tex]

I'm not sure how to go about doing this because I've been staring at:

[tex](cos(\beta)-1)x=-sin(\beta)e^{-i \alpha} y[/tex]

[tex]sin(\beta) e^{i \alpha} x = (-cos(\beta)-1) y[/tex]

for a while now and I'm not sure how to get the x and y values

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