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December 3, 2020 1:34 pmpts 30 pts
65. Let f (x) and g(x) be two non-zero polynomials over an arbitrary ring R. Then which is true ? A) deg S()+s()]= deg.S(e) + deg g (=) ) des[()+g()]s Mar[ deg / (w), deg s( (C) deg[()+ 8()]= Mar[ deg f(:), dog s()] (D) None of these 66. Let W be a subspace of the space R'. If dim W=0, then W is a: (A) line through the origin 5) plane through the origin (C) entire space R (D) point 67, The square matrIx A and its transpose have the . eigen values. A) same (B) different unique (D) None of these 68. Let Q be the set of ratipnal numbers. Then Q (V3 a+ b3 : a,b eQ is a vector space over Q with dimension A) (B) 2 (C) 3 (D) 4 69. Let T:U >V be a linear transformation from an n dimensional vector space U) to a Vector space v (F), then (A) dim N(T) + dim R (T)=0 (B) dim N(T) + dim R (T) = 2n (C) dim N(T) + dim R (T) =* (D) dim N (T)+ dim R (T) = n
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  • Mahendra devanda thankyou
    see attachment
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  • Deepak singh Best Answer
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