Question: Suppose that T: U V and S: V W are linear transformations, and that B, C and D are bases for U, V,

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.

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Suppose that B u 1 u 2 u 3 u m C v 1 v 2 v 3 v n and D w 1 w 2 w 3 w p For convenience set M M T BC ... View full answer

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