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arrow_back Find a linear map of the plane, \(A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) that does the following transformation of the letter \(\mathbf{F}\) (here the smaller \(\mathbf{F}\) is transformed to the larger one):

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a). Find a linear map of the plane, \(A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) that does the following transformation of the letter \(\mathbf{F}\) (here the smaller \(\mathbf{F}\) is transformed to the larger one):

 

transformation

b). Find a linear map of the plane that inverts this map, that is, it maps the larger \(\mathbf{F}\) to the smaller.

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