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Given w = T (v), where T is a linear transformation and w and v are vectors, why is it that we can write any coefficient of w, such as w_{1} as a linear combination of the coefficients of v? i.e. w_{1} = av_{1} + bv_{2} + cv_{3}
Supposably this is a consequence of the definition of linear transformations, but I don't see the connection.
Supposably this is a consequence of the definition of linear transformations, but I don't see the connection.