Monthly Archives: June 2013

Exercise 2.6.7. Describe the matrices representing the following transformations: i) projecting all vectors onto the – plane ii) reflecting all vectors through the – plane iii) rotating all vectors in the – plane by 90 degrees, leaving the axis unchanged … Continue reading →

Exercise 2.6.6. Suppose we have a transformation matrix This is a shearing transformation: it leaves unchanged any points for which and thus leaves unchanged the entire -axis. Describe how this transformation affects the -axis, including the points , , and … Continue reading →

Exercise 2.6.5. Suppose we have two points and and a third point halfway between the first two points. Show that for any linear transformation represented by a matrix the (transformed) point is halfway between and . Answer: If is halfway … Continue reading →