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## Homework Statement

Let ##f : \mathbb{R}^n \rightarrow \mathbb{R}^m## be a linear function. Suppose that with the standard bases for ##\mathbb{R}^n## and ##\mathbb{R}^m## the function ##f## is represented by the matrix ##A##. Let ##b_1, b_2, \ldots, b_n## be a new set of basis vectors for ##\mathbb{R}^n## and ##c_1, c_2, \ldots, c_m## be a new set of

basis vectors for ##\mathbb{R}^m##. What is the matrix that represents ##f## when the linear spaces are described in terms of the new basis vectors?

## Homework Equations

## The Attempt at a Solution

Suppose ##f : \mathbb{R}^n \rightarrow \mathbb{R}^n## is represented by the matrix ##A## when we describe ##\mathbb{R}^n## in terms of the standard basis vectors ##e_1, e_2, \ldots, e_n## and that we have a new set of basis vectors ##b_1, b_2, \ldots, b_n##. Then when ##\mathbb{R}^n## is described in terms of these new basis vectors the linear function ##f## will be represented by the matrix ##B^{-1}AB##.