Question

this is linear algebra question
In R^3 the orthogonal projections on the x-axis, y-axis, and z-axis are defined by
respectively.
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 on the coordinate axes are linear operators, and find their standard matrices.
(b) Show that if T:R^3toR^3 is an orthogonal projection on one of the coordinate axes, then for every vector x in R^3,the vectors T(X) and x-T(x) are orthogonal vectors.
(c) Make a sketch showing x and x-T(x) in the case where T is the orthogonal projection on the x-axis.

Answer 1

please answer the question