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Determine whether w is in the range of the linear operator T

T:R3 - R3: T (x,y,z) = (2x-y, x+z, y-z); w= (3,3,0)

Here is my solution:

T (3,3,0) = (2x3-3, 3+0, 3-0)

T (3,3,0) = (3, 3, 3) 

What I am doing wrong? And how to explain if it is in the range or not? Thank you! 

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1 Answer

2x    -y         = 3

x             +z = 3

         y    -z  = 0

Use row reduction or substitution to get x = 2, y = 1, z = 1.

T(2, 1, 1) = (3, 3, 0)

 

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