In parts (a) through (e) below, mark the statement True or False. Justify each answer
a) A linear transformation T: Rⁿ→Rᵐ is completely determined by its effect on the columns of the n x n identity matrix.

A. True. A transformation T is defined in terms of its effect on the columns of the n x n identity matrix because otherwise the standard matrix A would be
B. False. It is possible for more than one linear transformation to have the same effect on the columns of the n x n identity matrix. impossible to determine
C. True. The vector x can be written as a linear combination of the columns of the identity matrix. T is a linear transformation so T(x) can be written as a inear combination of the vectors T(e₁) and T(e₂).
D. False. The transformation is jointly determined by its effect on the columns of the nxn identity matrix and by the result of writing x as a linear combination of the columns of the standard matrix A.