Akshita Kaushik posted an Question
February 12, 2021 • 21:57 pm 30 points
  • IIT JAM
  • Mathematics (MA)

A1 a12 with complex entries such that a1 a22 let v be the set of 2 x 2 matrices a21 = 0. let w be the set of matrices in v with a2 +az1=0. then, under usual mat

a1 a12 with complex entries such that a1 a22 Let V be the set of 2 x 2 matrices a21 = 0. Let W be the set of matrices in V with a2 +az1=0. Then, under usual matrix addition and scalar multiplication, which of the following is(are) true? (b) W is a vector space over C (a) V is a vector space over C (c) V is a vector space over R (d) W is a vector space over R

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  • comment-profile-img>
    Sonu saini

    option C is also correct because if V is vector space over super field of any field then that must be vector space of that field

  • comment-profile-img>
    Piyush pachauri best-answer

    A,C,D are correct. Trace 0 matrix form vector space over C

  • comment-profile-img>
    Piyush pachauri

    Option B is not correct ,Take Matrix A such that a12 = a21=i ,other entries are 0 then it belongs to W but iA doesn't belong to W.

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