Chashokreddy18@gmail.com posted an Question
April 06, 2020 • 22:16 pm 30 points
  • CSIR NET
  • Mathematical Sciences

Linear algebra - prop of v.s can you explain how did we get last three steps in the proof?

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  • Chashokreddy18@gmail.com Tiwari

    Here why did we prove no.of elements in v.s?

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    there is no need to prove dimension when we have to prove subspace. But this concept is important thats why given.

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    Ujjawal vishal best-answer

    See, a matrix of order m*n has total 'mn' entries. Zp contains p elements {0,1,2....,(p-1)} . So, we have total p choices to fill 1st entry in matrix. Since, numbers can be same in matrix, 2nd place can also be filled in p ways. So, at each place we have p choice to fill. So, according to fundamental principal of counting ,total no of such m*n matrices = p*p*p*....*p (mn times) =p^mn hence, dimension of V = p^mn.

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