Let T is a linear operator ondefined by, T(x,y,z) = (3x+z, -2x+y, -x+2y+ 4z), thena)T is one-one and ontob)T is onto but not one-onec)T is invertibled)Trace T = 23Correct answer is option 'A,C,D'. Can you explain this answer?

Question

Answer

(on interchanging R₁ ↔ R₃)

⇒ x = y = 0 = z

⇒ Ker T = {(0,0,0}

⇒ T is one-one⇒ T is on to

⇒ T is invertible

Let B = {(1,0,0),(0,1,0),(0,0,1)} is an ordered basis of

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