Dimension of a matrix vectorspace

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SUMMARY

The dimension of the vector space V of n × m matrices over a field F is definitively n*m. An explicit basis for V consists of matrices that have a single entry of 1 at each position (i,j) where 1 ≤ i ≤ n and 1 ≤ j ≤ m, with all other entries being zero. This basis contains exactly n*m elements, confirming the dimension calculation. The simplicity of the problem may lead to doubts, but the solution is straightforward and correct.

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Homework Statement



Let V be the vector space of n × m matrices with entried in a field F . What is the dimension of V ? Give an explicit basis for V over F .

The Attempt at a Solution



The question is a little vague, but if I understand correctly, wouldn't the dimension of V simply be n*m? For the basis (it has m*n elements), would it simply be zero matrices with a 1 in the "ij" entry, starting at 1,1 and ending at n,m?
I feel like the question is just too easy, which is leading me to doubt my answer...
 
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That seems correct.
 

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