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...

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.

Expert Solution

Colby Messinger answered 7 months ago

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