Kunze Linear Algebra · Problem 3.1.11

Linear Transformations

Mathematics — Methods · zero-transformation-zero-matrix

Problem

Let VV be the space of n×1n \times 1 matrices over FF and let WW be the space of m×1m \times 1 matrices over FF. Let AA be a fixed m×nm \times n matrix over FF and let TT be the linear transformation from VV into WW defined by T(X)=AXT(X) = AX. Prove that TT is the zero transformation if and only if AA is the zero matrix.

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