I have projection matrix given below. I want you to completely setup the main camera in unity according to projection matrix $($rotation$,$ orientation etc., too. Do not miss them$).$ Do the full setup in unity script but If I need to do something manually, describe and explain it clearly. After that, I want you to convert $3$D world point $(132\mathrm{.}65,34\mathrm{.}76,1\mathrm{.}2)$ to $2$D pixel coordinate. Then convert the $2$D pixel you just found to $3$D world point coordinate again and check if the initial $3$D world point and your reconstructed $3$D world point are matched. If they are matched, the conversions correct.$$

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The key part of the task is that you will lose depth information while converting $3$D world point to $2$D pixel point. You must be able to obtain correct depth information again while converting $2$D pixel point to $3$D world point.

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Key words: world space, camera space, clip space, NDC$($Normalized Device Coordinates$),$ Screen Space, pixel coordinates, projection matrix, view matrix $($from world space to camera space$)$

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$$projectionMatrix $=$ new Matrix$4$x$4($

$$ new Vector$4(2\mathrm{.}69568618$e$+03$f$,2\mathrm{.}74645799$e$+02$f$,-7\mathrm{.}56550620$e$+02$f$,2\mathrm{.}37548448$e$+02$f$),$

$$ new Vector$4(-4\mathrm{.}33788713$e$+02$f$,2\mathrm{.}72324315$e$+03$f$,-5\mathrm{.}57043156$e$+02$f$,-1\mathrm{.}60581529$e$+03$f$),$

$$ new Vector$4(2\mathrm{.}40985090$e$-01$f$,2\mathrm{.}31194796$e$-01$f$,9\mathrm{.}42589653$e$-01$f$,-3\mathrm{.}64592433$e$-01$f$),$

$$ new Vector$4(0$f$,0$f$,0$f$,1$f$)//$ Padding row to make it a $4$x$4$ matrix

$)$;