Matrix Multiplication for Latin Squares

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This is for a project, so I could really use some insight!

We are working with Latin Squares, and below is the information regarding the data:

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Now, I don't understand what to do with Y=Xθ+e. I can't multiply Xθ, since one is 10x9, and the other is 1x10, and I feel like if I rearrange the matrices, I'm not doing what was intended, especially since I then need to add error, a 1x9 matrix.

Am I misreading the formula? How are these matrices supposed to interact?

Any help here would be great!!!