Question: Question: Lete 1 = (1,0,0) T , e 2 = (0,1, 0) T , e 3 = (0,0,1) T be the standard basis of R

Question:

Lete₁= (1,0,0)^T, e₂= (0,1, 0)^T, e₃= (0,0,1)^Tbe the standard basis ofR³. Consider a linear mapT:R³->R³satisfying T(x, y, z)^T= (0,0,0)^Twhenever 2x-y+z= 0.

(a) Show thatT ((1/2, 0, -1)^T)= (0,0,0)^Tand T(0, 1, 1)^T= (0, 0, 0)^T.

(b) Justify whetherTis an isomorphism using result from (a).

(d) Use your results ofT(e₁), T(e₂), T(e₃) to determine the image of an arbitrary vector

(x, y, z)^T

Question: Lete 1 = (1,0,0) T , e 2 = (0,1, 0) T ,

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