In R3 the orthogonal projections onto the x-axis, y-axis, and z-axis are T1(x, y, z) =
Chapter 4, Problem 40(choose chapter or problem)
In R3 the orthogonal projections onto the x-axis, y-axis, and z-axis are T1(x, y, z) = (x, 0, 0), T2(x, y, z) = (0, y, 0), T3(x, y, z) = (0, 0, z) respectively. (a) Show that the orthogonal projections onto the coordinate axes are (b) Show that if T : R3R3 is an orthogonal projection onto one of the coordinate axes, then for every vector x in R3, the vectors T(x) and x T(x) are orthogonal. (c) Make a sketch showing x and x T(x) in the case where T is the orthogonal projection onto the x-axis.
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