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...Linear transformations of the plane now that we re using matrices to represent ll nd ourselves en countering a wide range and it can become dicult keep track which do what in these notes develop tool box basic easily be remembered by their geometric properties focus on t r itself thus corresponding transformation perhaps most important fact mind as determine dierent is rst second columns are given e respectively where standard unit vectors scaling want consider every vector some factor k x kx for if then does nothing this case so matrix call identity size denote either i or when obvious any other scale have suppose two maps scales say means its representation should kk indeed check agrees with our notion multiplication representing composition trans formations figure orthogonal projection v onto w next d like projecting line first project one another take look at orthogonally mean displacement projwv seen wecanseethatproj will scalar multiple let s write proj kw since require nownotice...