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###### Swagat posted an Question
September 19, 2021 • 10:48 am 10 points
• IIT JAM
• Mathematics (MA)

# The dimension of the vector space v={a =[a,laxa a e c, a-ai over field r is (a) n b) n-1 d) (c)n-n 2

The dimension of the vector space V={A =[a,laxa a E C, a-ai over field R is (a) n b) n-1 d) (C)n-n 2

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• ##### Anonymous User

given set is set of skew symmetric matrix whose entry is complex . dim of skew symmetric matric is n(n-1)/2 but each entire is complex and dim.of complex is 2 so dim of V is ([n(n-1)/2]*2= n(n-1)

• ##### Anonymous User

solution is n(n-1

because elements of A is complex n digonal elements zero total n² elements in matrix so nonzero elements n²-n wich are complex but by skew symmetric property (n²-n)/2 are different complex .eeach complex contains two part real and imagemary so dim n²-n

if A is skew symmetric matrix of oder 2 than it can be express as sum of two matrix so number of elements in its bases 2

similarly for n number of elements in base n²-n

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