Question: Let T : V W be a linear transformation between finite-dimensional vector spaces V and W. Let B and C be bases for V

Let T : V → W be a linear transformation between finite-dimensional vector spaces V and W. Let B and C be bases for V and W, respectively, and let A = [T]_C←B.

If B′ and C′ are also bases for V and W, respectively, what is the relationship between [T]_C←B and [T]_C′←B?
Prove your assertion.

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