In: Advanced Math
Consider a transformation ?:ℝ3→ℝ3T:R3→R3 defined by
?(?,?,?)=(?+?+?, 2?+?, ?−2?+?).T(x,y,z)=(x+y+z, 2x+y, x−2y+z).
(a) Find the standard matrix of ?T.
(b) Is ?T a linear transformation? Explain.
(c) Is ?T invertible?
(d) Find the image of (2,−1,1)(2,−1,1) under ?T.