Let T: R3 -> R4 be the linear transformation defined as follows:....?
T(x,y,z) = (x-y+3z, -2x+2y-5z, 3x-3y+7z, -x+y+2z)
1. Find a formula for all elements in ker(T).
2. Is there an (x,y,z) in R3 so that T(x,y,z) = (1,-1,1,4)? (You do not need to find (x,y,z) if it exists, but explain how you know you answer is correct.)
3. Is there an (x,y,z) in R3 so that T(x,y,z) = (1,2,3,4)? (You do not need to find (x,y,z) if it exists, but explain how you know you answer is correct.)

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