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Divam Kumar posted an Question
December 03, 2020 • 20:02 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Sotative figw wito unity and let a be an ideal of k.thep w/hoh one 21. let r be a com is drae (a) rais an integgal domais a is prime ideal. (b)aisprime ideal ri

sotative figw wito unity and let A be an ideal of K.Thep w/hoh one 21. Let R be a com is Drae (A) RAis an integgal domais A is prime ideal. (B)Aisprime ideal RIA is an integral domain. (C) Both (A) and (# (D) None of these 22. Let T: R Rbe a linear ormation given by: Then (a, b, c) for all (a, b, c) e R is: A) (a -b,b - c,a) T1,0, 0) 1,0, 1,71,9)0,-1,0; T (0, 0, 1) (0, 1, 0) (B) (a+b,- b + c,a) (C) (a+b, b - c,a) (D) None of these 23. Let T R Rbe a linear transformation given y T (x,y) = (z+ y,7-7.9) 7(2,9) e R<. Then dimension of range of T is A) 1 (B) 2 (C) 3 (D) None of these 24. Let U and V be vector spaces over the field F and let T be a linear transfomaion from U into V. Suppose that Uis finite dimensional, then (A) rank (T)+ nullity T)- dim () (B) rank (T)+nullity (CT)-dim (U) (C) rank (T)-nullity (T)= dim (U) (D) rank (T)- nullity (T)=dim (V) 25. Let T: U V be a lincar transfomation. Then choose the correct statement (A) Tis one-one Ker (T)= {0} (B) Ker (T)= {0} =Tis one-one (C) Tis one-one Ker (T)= {0} (D) None of these

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