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a. (1.5 points) Using the $Z−Y−X(α−β−γ)$ Euler angle convention, write a MATLAB program to calculate the rotation matrix $R$ when the user enters the Euler angles $α−β−γ$. Test for two examples i) $α=10_{∘},α=30_{∘}, β=20_{∘},β=90_{∘}, γ=30_{∘}.γ=−55_{∘}. $ b. (1.5 points) Write a MATLAB program to calculate the Euler angles $α−β−γ$ when the user inputs the rotation matrix $R$ (the inverse problem). Demonstrate this inverse solution for the two cases from part 2.2.a.

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