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The issue was with the matrix multiplication library that I was using. I misunderstood one of the functions which led me to this nonsensical transformation matrix. Multiplying the matrices I added with my edit will output the correct transformation.
[[ 0.9829962 -0.1535926 0.10063695 -0.74704943]
[ 0.02044092 -0.45311975 -0.89121528 1.09928188]
[ 0.18248466 0.87811834 -0.44227541 3.86385995]
[ 0. 0. 0. 1. ]]
