Construct a new solution to Exercise B.T50 along the following outline. From the n × n matrix A, construct the linear transformation T: Cn ? Cn, T (x) = Ax. Use Theorem NI, Theorem IMILT and Theorem ILTIS to translate between the nonsingularity of A and the surjectivity/injectivity of T. Then apply Theorem ILTB and Theorem SLTB to connect these properties with bases.
This question was answered on: Jul 11, 2017
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