Question: It is a known theorem that if T : R-R is a linear transformation and A is the standard matrix for T, then T maps

It is a known theorem that if T : R"-R" is a linear transformation and A is the standard matrix for T, then T maps R" onto R if and only if the ' : = t= columns of Aspan R", and T is one-to-one if and only if the columns of A are linearly independent. Applying this theorem to the transformation T , it canbe concluded that T | is | iy]

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