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Linear maps \(F(X)=A X\), where \(A\) is a matrix, have the property that \(F(0)=A 0=0\), so they necessarily leave the origin fixed. It is simple to extend this to include a translation,

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Linear maps \(F(X)=A X\), where \(A\) is a matrix, have the property that \(F(0)=A 0=0\), so they necessarily leave the origin fixed. It is simple to extend this to include a translation,
\[
F(X)=V+A X,
\]
where \(V\) is a vector. Note that \(F(0)=V\).
Find the vector \(V\) and the matrix \(A\) that describe each of the following mappings [here the light blue \(F\) is mapped to the dark red \(F]\).

trans

in Mathematics by Platinum (102k points) | 282 views

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