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Deepak Patra posted an Question
January 04, 2022 • 17:58 pm 30 points
  • IIT JAM
  • Mathematics (MA)

5. let m,(k) denote the space of all nxn matrices with entries from afield k. fix a non-singular matrix a= (4) e m,(k) and map consider the linear t:m,(k) -m,(k

5. Let M,(K) denote the space of all nxn matrices with entries from afield K. Fix a non-singular matrix A= (4) e M,(K) and map consider the linear T:M,(K) -M,(K) given by: T(X) = AX. Then (a.) Trace (T)=n2iAu Aij b.) Trace (T)=Zi2ji A .(c.) Rank of T is n (d.) T is non-singular

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  • Anonymous User best-answer

    D check attachment

    cropped7178961238365944005.jpg
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    sir c can also be the ans ... as T is non singular dimension of A is n²

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    if u take identity matrix then T=I rank of T ≠n²

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    understand

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