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Consider the following functions which map Rn to Rn.
(a) T multiplies the jth component of~x by a nonzero number b.
(b) T replaces the ith component of~x with b times the jth component added to the ith component.
(c) T switches the ith and jth components.
Show these functions are linear transformations and describe their matrices A such that T (~x).
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