Let X and Y be finite-dimensional vector spaces. Let ##T:X\to Y## be a linear transformation. Let ##A=(e_1,\dots,e_n)## and ##B=(f_1,\dots,f_m)## be ordered bases for X and Y respectively. (An ordered basis for an n-dimensional vector space is just an n-tuple whose components are the elements of a basis). For each ##y\in Y##, there’s a unique m-tuple…