IIT JAM
Akshita kaushik Asked a Question
February 12, 2021 4:27 pmpts 30 pts
  • 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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  • Sonu saini thankyou
    any doubt you can ask
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  • 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
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  • Sonu saini Best Answer
    see attachment
    • cropped5205516708151953348.jpg
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  • Piyush
    Any doubt then you can ask
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  • Piyush thankyou
    A,C,D are correct. Trace 0 matrix form vector space over C
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  • Sonu saini
    answer A and D is correct
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  • Piyush
    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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