Suppose that T: U → V and S: V → W are linear transformations, and that B, C and D are bases for U, V, and W. Using only Definition MR define matrix representations for T and S. Using these two definitions, and Definition MR, derive a matrix representation for the composition S ο T in terms of the entries of the matrices MTB,C and MSC,D. Explain how you would use this result to motivate a definition for matrix multiplication that is strikingly similar to Theorem EMP.